%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : HWV003-2 : TPTP v9.2.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n014.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 11.07s 7.33s
% Output : CNFRefutation 11.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 35
% Syntax : Number of clauses : 359 ( 357 unt; 0 nHn; 233 RR)
% Number of literals : 361 ( 360 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 16 con; 0-2 aty)
% Number of variables : 209 ( 32 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t6,negated_conjecture,
not(and(t4,t5)) = t6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6) ).
cnf(and_commutative,axiom,
and(X1,X2) = and(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_commutative) ).
cnf(and_absorption,axiom,
and(X1,or(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_absorption) ).
cnf(or_commutative,axiom,
or(X1,X2) = or(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_commutative) ).
cnf(or_demorgan,axiom,
not(or(X1,X2)) = and(not(X1),not(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_demorgan) ).
cnf(or_absorption,axiom,
or(X1,and(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_absorption) ).
cnf(not_involution,axiom,
not(not(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_involution) ).
cnf(and_associative,axiom,
and(and(X1,X2),X3) = and(X1,and(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_associative) ).
cnf(sum,negated_conjecture,
not(and(t6,t7)) = sum,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum) ).
cnf(t4,negated_conjecture,
not(and(t2,t3)) = t4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4) ).
cnf(and_demorgan,axiom,
not(and(X1,X2)) = or(not(X1),not(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_demorgan) ).
cnf(t5,negated_conjecture,
not(and(t4,cin)) = t5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5) ).
cnf(and_distributive,axiom,
or(X1,and(X2,X3)) = and(or(X1,X2),or(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_distributive) ).
cnf(t2,negated_conjecture,
not(and(a,t1)) = t2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2) ).
cnf(or_distributive,axiom,
and(X1,or(X2,X3)) = or(and(X1,X2),and(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_distributive) ).
cnf(or_complement,axiom,
or(X1,not(X1)) = ll1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_complement) ).
cnf(or_associative,axiom,
or(or(X1,X2),X3) = or(X1,or(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_associative) ).
cnf(t1,negated_conjecture,
not(and(a,b)) = t1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1) ).
cnf(and_identity,axiom,
and(X1,ll1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_identity) ).
cnf(t7,negated_conjecture,
not(and(t5,cin)) = t7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7) ).
cnf(or_identity,axiom,
or(X1,ll0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_identity) ).
cnf(and_complement,axiom,
and(X1,not(X1)) = ll0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_complement) ).
cnf(t3,negated_conjecture,
not(and(b,t1)) = t3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3) ).
cnf(or_boundedness,axiom,
or(X1,ll1) = ll1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_boundedness) ).
cnf(and_boundedness,axiom,
and(X1,ll0) = ll0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_boundedness) ).
cnf(carry,negated_conjecture,
not(and(t1,t5)) = carry,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',carry) ).
cnf(ll1_inverse,axiom,
not(ll1) = ll0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ll1_inverse) ).
cnf(and_idempotent,axiom,
and(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_idempotent) ).
cnf(or_idempotent,axiom,
or(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_idempotent) ).
cnf(carry_def,negated_conjecture,
or(and(cin,or(a,b)),and(not(cin),and(a,b))) = carry_def,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',carry_def) ).
cnf(sum_def,negated_conjecture,
xor(xor(a,b),cin) = sum_def,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_def) ).
cnf(xor_definition,axiom,
or(and(not(X1),X2),and(X1,not(X2))) = xor(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_definition) ).
cnf(xor_associative,axiom,
xor(X1,xor(X2,X3)) = xor(xor(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_associative) ).
cnf(ll0_inverse,axiom,
not(ll0) = ll1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ll0_inverse) ).
cnf(prove_circuit,negated_conjecture,
( sum != sum_def
| carry != carry_def ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_circuit) ).
cnf(c_0_35,negated_conjecture,
not(and(t4,t5)) = t6,
t6 ).
cnf(c_0_36,axiom,
and(X1,X2) = and(X2,X1),
and_commutative ).
cnf(c_0_37,axiom,
and(X1,or(X1,X2)) = X1,
and_absorption ).
cnf(c_0_38,axiom,
or(X1,X2) = or(X2,X1),
or_commutative ).
cnf(c_0_39,axiom,
not(or(X1,X2)) = and(not(X1),not(X2)),
or_demorgan ).
cnf(c_0_40,axiom,
or(X1,and(X1,X2)) = X1,
or_absorption ).
cnf(c_0_41,axiom,
not(not(X1)) = X1,
not_involution ).
cnf(c_0_42,negated_conjecture,
not(and(t5,t4)) = t6,
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,plain,
and(X1,or(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,axiom,
and(and(X1,X2),X3) = and(X1,and(X2,X3)),
and_associative ).
cnf(c_0_45,plain,
and(not(X1),not(and(X1,X2))) = not(X1),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,negated_conjecture,
not(and(t6,t7)) = sum,
sum ).
cnf(c_0_47,negated_conjecture,
not(t6) = and(t5,t4),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,plain,
and(X1,and(X2,X1)) = and(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_40]),c_0_44]) ).
cnf(c_0_49,negated_conjecture,
and(t5,and(t4,sum)) = and(t5,t4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_44]),c_0_47]) ).
cnf(c_0_50,negated_conjecture,
not(and(t2,t3)) = t4,
t4 ).
cnf(c_0_51,plain,
or(X1,and(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_40,c_0_36]) ).
cnf(c_0_52,negated_conjecture,
and(t4,and(sum,and(t5,t4))) = and(t4,and(t5,sum)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_44]),c_0_44]),c_0_36]) ).
cnf(c_0_53,negated_conjecture,
not(t4) = and(t2,t3),
inference(spm,[status(thm)],[c_0_41,c_0_50]) ).
cnf(c_0_54,axiom,
not(and(X1,X2)) = or(not(X1),not(X2)),
and_demorgan ).
cnf(c_0_55,negated_conjecture,
not(and(t4,cin)) = t5,
t5 ).
cnf(c_0_56,plain,
or(X1,and(X2,and(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_51,c_0_44]) ).
cnf(c_0_57,negated_conjecture,
and(t2,and(t3,not(and(t4,and(t5,sum))))) = and(t2,t3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_52]),c_0_53]),c_0_44]),c_0_53]) ).
cnf(c_0_58,plain,
or(not(X1),X2) = not(and(X1,not(X2))),
inference(spm,[status(thm)],[c_0_54,c_0_41]) ).
cnf(c_0_59,axiom,
or(X1,and(X2,X3)) = and(or(X1,X2),or(X1,X3)),
and_distributive ).
cnf(c_0_60,negated_conjecture,
not(and(cin,t4)) = t5,
inference(rw,[status(thm)],[c_0_55,c_0_36]) ).
cnf(c_0_61,negated_conjecture,
not(and(t4,and(t5,sum))) = t6,
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_56,c_0_57]),c_0_58]),c_0_50]),c_0_44]),c_0_44]),c_0_36]),c_0_49]),c_0_48]),c_0_36]),c_0_42]) ).
cnf(c_0_62,negated_conjecture,
not(and(a,t1)) = t2,
t2 ).
cnf(c_0_63,plain,
or(X1,and(X2,and(X1,X3))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_51]),c_0_37]),c_0_44]) ).
cnf(c_0_64,negated_conjecture,
and(t5,not(cin)) = not(cin),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_60]),c_0_36]) ).
cnf(c_0_65,negated_conjecture,
and(t4,and(t5,sum)) = and(t5,t4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_61]),c_0_47]) ).
cnf(c_0_66,axiom,
and(X1,or(X2,X3)) = or(and(X1,X2),and(X1,X3)),
or_distributive ).
cnf(c_0_67,negated_conjecture,
not(t2) = and(a,t1),
inference(spm,[status(thm)],[c_0_41,c_0_62]) ).
cnf(c_0_68,axiom,
or(X1,not(X1)) = ll1,
or_complement ).
cnf(c_0_69,axiom,
or(or(X1,X2),X3) = or(X1,or(X2,X3)),
or_associative ).
cnf(c_0_70,negated_conjecture,
or(t5,and(X1,not(cin))) = t5,
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_71,negated_conjecture,
and(t5,or(t4,sum)) = and(t5,sum),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_65]),c_0_66]),c_0_38]) ).
cnf(c_0_72,negated_conjecture,
not(t5) = and(cin,t4),
inference(spm,[status(thm)],[c_0_41,c_0_60]) ).
cnf(c_0_73,negated_conjecture,
and(a,and(t1,t4)) = and(a,t1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_50]),c_0_67]),c_0_44]),c_0_67]) ).
cnf(c_0_74,negated_conjecture,
not(and(a,b)) = t1,
t1 ).
cnf(c_0_75,plain,
or(X1,or(X2,and(not(X1),not(X2)))) = ll1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_39]),c_0_69]) ).
cnf(c_0_76,negated_conjecture,
or(t5,and(not(cin),X1)) = t5,
inference(spm,[status(thm)],[c_0_70,c_0_36]) ).
cnf(c_0_77,axiom,
and(X1,ll1) = X1,
and_identity ).
cnf(c_0_78,negated_conjecture,
not(sum) = and(t6,t7),
inference(spm,[status(thm)],[c_0_41,c_0_46]) ).
cnf(c_0_79,negated_conjecture,
not(and(t5,cin)) = t7,
t7 ).
cnf(c_0_80,axiom,
or(X1,ll0) = X1,
or_identity ).
cnf(c_0_81,negated_conjecture,
and(cin,and(t4,not(and(t5,sum)))) = and(cin,t4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_71]),c_0_72]),c_0_44]),c_0_72]) ).
cnf(c_0_82,plain,
not(and(not(X1),not(X2))) = or(X1,X2),
inference(spm,[status(thm)],[c_0_41,c_0_39]) ).
cnf(c_0_83,negated_conjecture,
and(t1,and(t4,and(a,t1))) = and(t1,and(a,t4)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_73]),c_0_44]),c_0_44]),c_0_36]) ).
cnf(c_0_84,negated_conjecture,
not(t1) = and(a,b),
inference(spm,[status(thm)],[c_0_41,c_0_74]) ).
cnf(c_0_85,negated_conjecture,
or(cin,t5) = ll1,
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_86,plain,
and(ll1,X1) = X1,
inference(spm,[status(thm)],[c_0_77,c_0_36]) ).
cnf(c_0_87,axiom,
and(X1,not(X1)) = ll0,
and_complement ).
cnf(c_0_88,negated_conjecture,
or(sum,and(t6,t7)) = ll1,
inference(spm,[status(thm)],[c_0_68,c_0_78]) ).
cnf(c_0_89,negated_conjecture,
not(and(cin,t5)) = t7,
inference(rw,[status(thm)],[c_0_79,c_0_36]) ).
cnf(c_0_90,plain,
or(ll0,X1) = X1,
inference(spm,[status(thm)],[c_0_80,c_0_38]) ).
cnf(c_0_91,negated_conjecture,
or(and(cin,t4),and(t4,not(and(t5,sum)))) = and(t4,not(and(t5,sum))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_81]),c_0_38]) ).
cnf(c_0_92,plain,
or(and(X1,X2),and(X2,X3)) = and(X2,or(X1,X3)),
inference(spm,[status(thm)],[c_0_66,c_0_36]) ).
cnf(c_0_93,plain,
or(X1,not(X2)) = not(and(not(X1),X2)),
inference(spm,[status(thm)],[c_0_82,c_0_41]) ).
cnf(c_0_94,plain,
and(X1,and(X2,X3)) = and(X3,and(X1,X2)),
inference(spm,[status(thm)],[c_0_36,c_0_44]) ).
cnf(c_0_95,negated_conjecture,
and(a,and(b,not(and(t1,and(a,t4))))) = and(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_83]),c_0_84]),c_0_44]),c_0_84]) ).
cnf(c_0_96,negated_conjecture,
not(and(b,t1)) = t3,
t3 ).
cnf(c_0_97,plain,
or(X1,or(X2,or(X1,and(X2,X3)))) = or(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_59]),c_0_69]) ).
cnf(c_0_98,negated_conjecture,
or(t6,and(t5,t4)) = ll1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_42]),c_0_38]) ).
cnf(c_0_99,axiom,
or(X1,ll1) = ll1,
or_boundedness ).
cnf(c_0_100,negated_conjecture,
or(cin,and(t5,X1)) = or(cin,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_85]),c_0_86]) ).
cnf(c_0_101,negated_conjecture,
and(t5,and(t4,t6)) = ll0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_42]),c_0_44]) ).
cnf(c_0_102,negated_conjecture,
or(sum,and(t6,and(t7,X1))) = or(sum,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_88]),c_0_44]),c_0_86]) ).
cnf(c_0_103,axiom,
and(X1,ll0) = ll0,
and_boundedness ).
cnf(c_0_104,negated_conjecture,
not(t7) = and(cin,t5),
inference(spm,[status(thm)],[c_0_41,c_0_89]) ).
cnf(c_0_105,plain,
and(X1,not(and(X1,not(X2)))) = and(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_87]),c_0_58]),c_0_90]) ).
cnf(c_0_106,negated_conjecture,
and(t4,not(and(sum,not(cin)))) = and(t4,not(and(t5,sum))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92]),c_0_93]),c_0_94]),c_0_36]),c_0_64]) ).
cnf(c_0_107,negated_conjecture,
and(a,and(b,t2)) = and(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_94]),c_0_36]),c_0_73]),c_0_62]) ).
cnf(c_0_108,negated_conjecture,
or(t2,and(a,t1)) = ll1,
inference(spm,[status(thm)],[c_0_68,c_0_67]) ).
cnf(c_0_109,negated_conjecture,
and(t3,not(b)) = not(b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_96]),c_0_36]) ).
cnf(c_0_110,negated_conjecture,
or(t5,t6) = ll1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99]),c_0_99]),c_0_38]) ).
cnf(c_0_111,negated_conjecture,
or(cin,and(t4,t6)) = cin,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_80]) ).
cnf(c_0_112,negated_conjecture,
and(cin,and(t4,t6)) = and(cin,t4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_42]),c_0_72]),c_0_44]),c_0_72]) ).
cnf(c_0_113,negated_conjecture,
or(sum,and(cin,t5)) = sum,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_87]),c_0_103]),c_0_80]),c_0_104]) ).
cnf(c_0_114,negated_conjecture,
and(t4,and(sum,not(cin))) = and(t5,t4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_105]),c_0_94]),c_0_36]),c_0_49]) ).
cnf(c_0_115,negated_conjecture,
or(and(a,b),and(b,t2)) = and(b,t2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_107]),c_0_38]) ).
cnf(c_0_116,negated_conjecture,
or(a,t2) = ll1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_108]),c_0_99]),c_0_99]),c_0_38]) ).
cnf(c_0_117,negated_conjecture,
or(t3,and(X1,not(b))) = t3,
inference(spm,[status(thm)],[c_0_63,c_0_109]) ).
cnf(c_0_118,negated_conjecture,
or(t5,and(X1,t6)) = or(t5,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_110]),c_0_77]) ).
cnf(c_0_119,negated_conjecture,
and(t4,t6) = and(cin,t4),
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_43,c_0_111]),c_0_44]),c_0_36]),c_0_94]),c_0_36]),c_0_112]) ).
cnf(c_0_120,negated_conjecture,
or(t5,and(cin,t4)) = ll1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_60]),c_0_38]) ).
cnf(c_0_121,negated_conjecture,
and(cin,and(t5,sum)) = and(cin,t5),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_113]),c_0_44]) ).
cnf(c_0_122,negated_conjecture,
not(and(cin,t6)) = not(cin),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_114]),c_0_58]),c_0_42]) ).
cnf(c_0_123,negated_conjecture,
and(b,t2) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_115,c_0_92]),c_0_116]),c_0_77]) ).
cnf(c_0_124,negated_conjecture,
and(t1,not(and(b,t2))) = not(and(b,t2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_115]),c_0_74]) ).
cnf(c_0_125,negated_conjecture,
or(t3,and(not(b),X1)) = t3,
inference(spm,[status(thm)],[c_0_117,c_0_36]) ).
cnf(c_0_126,negated_conjecture,
and(t2,and(t3,t6)) = and(t2,t3),
inference(rw,[status(thm)],[c_0_57,c_0_61]) ).
cnf(c_0_127,negated_conjecture,
or(t4,and(t2,t3)) = ll1,
inference(spm,[status(thm)],[c_0_68,c_0_53]) ).
cnf(c_0_128,plain,
and(or(X1,X2),or(X3,X1)) = or(X1,and(X2,X3)),
inference(spm,[status(thm)],[c_0_59,c_0_38]) ).
cnf(c_0_129,negated_conjecture,
or(t6,sum) = ll1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_88]),c_0_99]),c_0_99]),c_0_38]) ).
cnf(c_0_130,plain,
and(or(X1,X2),or(X2,X3)) = or(X2,and(X1,X3)),
inference(spm,[status(thm)],[c_0_59,c_0_38]) ).
cnf(c_0_131,negated_conjecture,
or(t5,t4) = ll1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_120]) ).
cnf(c_0_132,negated_conjecture,
or(and(cin,t5),and(t5,sum)) = and(t5,sum),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_121]),c_0_38]) ).
cnf(c_0_133,negated_conjecture,
and(cin,t6) = cin,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_122]),c_0_41]) ).
cnf(c_0_134,negated_conjecture,
and(t7,not(cin)) = not(cin),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_89]),c_0_36]) ).
cnf(c_0_135,negated_conjecture,
or(b,t2) = t2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_123]),c_0_38]) ).
cnf(c_0_136,plain,
and(X1,and(X2,X3)) = and(X2,and(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_36]),c_0_44]) ).
cnf(c_0_137,negated_conjecture,
and(t1,not(b)) = not(b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_124,c_0_123]),c_0_123]) ).
cnf(c_0_138,negated_conjecture,
not(t3) = and(b,t1),
inference(spm,[status(thm)],[c_0_41,c_0_96]) ).
cnf(c_0_139,negated_conjecture,
or(b,t3) = ll1,
inference(spm,[status(thm)],[c_0_75,c_0_125]) ).
cnf(c_0_140,negated_conjecture,
or(and(t2,t3),and(t3,t6)) = and(t3,t6),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_126]),c_0_38]) ).
cnf(c_0_141,negated_conjecture,
or(t4,t2) = ll1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_127]),c_0_99]),c_0_99]) ).
cnf(c_0_142,negated_conjecture,
or(sum,and(X1,t6)) = or(sum,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_77]) ).
cnf(c_0_143,negated_conjecture,
or(t4,and(t5,X1)) = or(t4,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_86]) ).
cnf(c_0_144,negated_conjecture,
and(t5,or(cin,sum)) = and(t5,sum),
inference(rw,[status(thm)],[c_0_132,c_0_92]) ).
cnf(c_0_145,plain,
or(X1,or(X2,X3)) = or(X2,or(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_38]),c_0_69]) ).
cnf(c_0_146,negated_conjecture,
or(cin,or(t4,sum)) = or(cin,sum),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_71]),c_0_100]) ).
cnf(c_0_147,negated_conjecture,
or(cin,t6) = t6,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_133]),c_0_38]) ).
cnf(c_0_148,negated_conjecture,
or(t7,and(X1,not(cin))) = t7,
inference(spm,[status(thm)],[c_0_63,c_0_134]) ).
cnf(c_0_149,negated_conjecture,
and(a,not(b)) = and(a,t1),
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_39,c_0_135]),c_0_67]),c_0_67]),c_0_94]),c_0_36]),c_0_136]),c_0_137]) ).
cnf(c_0_150,negated_conjecture,
or(t3,and(b,t1)) = ll1,
inference(spm,[status(thm)],[c_0_68,c_0_138]) ).
cnf(c_0_151,negated_conjecture,
not(and(t1,t5)) = carry,
carry ).
cnf(c_0_152,negated_conjecture,
or(b,and(t3,X1)) = or(b,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_139]),c_0_86]) ).
cnf(c_0_153,negated_conjecture,
and(t3,or(t2,t6)) = and(t3,t6),
inference(rw,[status(thm)],[c_0_140,c_0_92]) ).
cnf(c_0_154,negated_conjecture,
or(t2,and(t4,X1)) = or(t2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_141]),c_0_86]) ).
cnf(c_0_155,negated_conjecture,
or(t2,and(X1,t4)) = or(t2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_141]),c_0_77]) ).
cnf(c_0_156,negated_conjecture,
or(sum,and(cin,t4)) = or(t4,sum),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_119]),c_0_38]) ).
cnf(c_0_157,negated_conjecture,
or(t4,sum) = or(cin,sum),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_143]),c_0_145]),c_0_146]) ).
cnf(c_0_158,axiom,
not(ll1) = ll0,
ll1_inverse ).
cnf(c_0_159,negated_conjecture,
and(t4,not(cin)) = and(t5,t4),
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_39,c_0_147]),c_0_47]),c_0_47]),c_0_94]),c_0_36]),c_0_64]) ).
cnf(c_0_160,negated_conjecture,
or(t7,and(not(cin),X1)) = t7,
inference(spm,[status(thm)],[c_0_148,c_0_36]) ).
cnf(c_0_161,negated_conjecture,
or(t4,and(X1,t2)) = or(t4,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_141]),c_0_77]) ).
cnf(c_0_162,negated_conjecture,
and(a,t2) = and(a,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_149]),c_0_62]) ).
cnf(c_0_163,negated_conjecture,
or(t3,and(b,and(t1,X1))) = or(t3,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_150]),c_0_86]),c_0_44]) ).
cnf(c_0_164,negated_conjecture,
or(t3,and(X1,b)) = or(t3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_139]),c_0_77]) ).
cnf(c_0_165,negated_conjecture,
or(t1,and(a,b)) = ll1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_74]),c_0_38]) ).
cnf(c_0_166,plain,
or(ll1,X1) = ll1,
inference(spm,[status(thm)],[c_0_99,c_0_38]) ).
cnf(c_0_167,negated_conjecture,
and(a,and(b,carry)) = and(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_151]),c_0_84]),c_0_44]),c_0_84]) ).
cnf(c_0_168,negated_conjecture,
or(b,or(t2,t6)) = or(b,t6),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_152]) ).
cnf(c_0_169,negated_conjecture,
or(t2,t6) = or(cin,t2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_119]),c_0_155]),c_0_38]) ).
cnf(c_0_170,negated_conjecture,
or(sum,and(cin,t4)) = or(cin,sum),
inference(rw,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_171,negated_conjecture,
and(t5,and(t4,and(t6,t7))) = ll0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_129]),c_0_158]),c_0_47]),c_0_78]),c_0_44]) ).
cnf(c_0_172,negated_conjecture,
or(t7,and(t5,t4)) = t7,
inference(spm,[status(thm)],[c_0_148,c_0_159]) ).
cnf(c_0_173,negated_conjecture,
or(cin,t7) = ll1,
inference(spm,[status(thm)],[c_0_75,c_0_160]) ).
cnf(c_0_174,negated_conjecture,
or(t4,and(a,b)) = or(a,t4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_38]) ).
cnf(c_0_175,negated_conjecture,
and(t2,not(a)) = not(a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_62]),c_0_36]) ).
cnf(c_0_176,negated_conjecture,
or(a,t3) = t3,
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_163,c_0_87]),c_0_103]),c_0_80]),c_0_84]),c_0_164]),c_0_38]) ).
cnf(c_0_177,negated_conjecture,
or(t1,or(and(a,b),X1)) = ll1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_165]),c_0_166]) ).
cnf(c_0_178,negated_conjecture,
or(and(a,b),and(b,carry)) = and(b,carry),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_167]),c_0_38]) ).
cnf(c_0_179,plain,
or(X1,or(X2,X1)) = or(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_37]),c_0_69]) ).
cnf(c_0_180,negated_conjecture,
or(b,or(cin,t2)) = or(b,t6),
inference(rw,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_181,negated_conjecture,
and(t1,not(a)) = not(a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_74]),c_0_36]) ).
cnf(c_0_182,negated_conjecture,
or(sum,and(t6,X1)) = or(sum,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_129]),c_0_86]) ).
cnf(c_0_183,negated_conjecture,
and(t6,not(cin)) = and(t5,and(t6,t7)),
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(spm,[status(thm)],[c_0_39,c_0_170]),c_0_39]),c_0_78]),c_0_78]),c_0_60]),c_0_44]),c_0_36]),c_0_136]),c_0_94]),c_0_36]),c_0_136]),c_0_134]) ).
cnf(c_0_184,negated_conjecture,
or(sum,and(X1,and(t6,t7))) = or(sum,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_88]),c_0_77]) ).
cnf(c_0_185,negated_conjecture,
and(cin,and(t6,X1)) = and(cin,X1),
inference(spm,[status(thm)],[c_0_44,c_0_133]) ).
cnf(c_0_186,negated_conjecture,
or(cin,and(t4,and(t6,t7))) = cin,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_171]),c_0_80]) ).
cnf(c_0_187,negated_conjecture,
and(t5,and(t4,t7)) = and(t5,t4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_172]),c_0_44]) ).
cnf(c_0_188,plain,
or(and(X1,X2),and(X3,X1)) = and(X1,or(X2,X3)),
inference(spm,[status(thm)],[c_0_66,c_0_36]) ).
cnf(c_0_189,negated_conjecture,
or(t7,and(cin,t5)) = ll1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_89]),c_0_38]) ).
cnf(c_0_190,negated_conjecture,
or(t7,and(cin,X1)) = or(t7,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_173]),c_0_86]) ).
cnf(c_0_191,negated_conjecture,
and(t4,and(t2,t3)) = ll0,
inference(spm,[status(thm)],[c_0_87,c_0_53]) ).
cnf(c_0_192,plain,
and(ll0,X1) = ll0,
inference(spm,[status(thm)],[c_0_103,c_0_36]) ).
cnf(c_0_193,negated_conjecture,
and(t3,not(a)) = and(t1,and(t2,t3)),
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_39,c_0_174]),c_0_39]),c_0_53]),c_0_53]),c_0_74]),c_0_44]),c_0_36]),c_0_136]),c_0_94]),c_0_36]),c_0_175]) ).
cnf(c_0_194,negated_conjecture,
and(a,t3) = a,
inference(spm,[status(thm)],[c_0_37,c_0_176]) ).
cnf(c_0_195,negated_conjecture,
or(t1,and(b,carry)) = ll1,
inference(spm,[status(thm)],[c_0_177,c_0_178]) ).
cnf(c_0_196,negated_conjecture,
and(t3,or(cin,t2)) = and(t3,t6),
inference(rw,[status(thm)],[c_0_153,c_0_169]) ).
cnf(c_0_197,negated_conjecture,
or(cin,t2) = or(b,t6),
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_179,c_0_180]),c_0_69]),c_0_69]),c_0_38]),c_0_135]),c_0_145]),c_0_169]),c_0_180]),c_0_145]),c_0_147]) ).
cnf(c_0_198,negated_conjecture,
and(b,not(a)) = and(b,t1),
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_39,c_0_176]),c_0_138]),c_0_138]),c_0_94]),c_0_36]),c_0_136]),c_0_181]) ).
cnf(c_0_199,axiom,
and(X1,X1) = X1,
and_idempotent ).
cnf(c_0_200,negated_conjecture,
or(t6,and(t5,X1)) = or(t6,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_110]),c_0_86]) ).
cnf(c_0_201,negated_conjecture,
or(t5,sum) = not(and(cin,t7)),
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_182,c_0_183]),c_0_184]),c_0_38]),c_0_93]),c_0_78]),c_0_44]),c_0_36]),c_0_136]),c_0_185]) ).
cnf(c_0_202,negated_conjecture,
and(cin,and(t4,and(t6,t7))) = and(t4,and(t6,t7)),
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_43,c_0_186]),c_0_44]),c_0_44]),c_0_36]),c_0_136]),c_0_136]) ).
cnf(c_0_203,negated_conjecture,
and(t4,or(t5,t7)) = and(t4,t7),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_187]),c_0_188]),c_0_38]) ).
cnf(c_0_204,negated_conjecture,
or(t5,t7) = ll1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_189,c_0_190]),c_0_38]) ).
cnf(c_0_205,negated_conjecture,
or(a,t1) = ll1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_165]),c_0_99]),c_0_99]),c_0_38]) ).
cnf(c_0_206,negated_conjecture,
and(t4,and(t2,and(t3,X1))) = ll0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_191]),c_0_192]),c_0_44]) ).
cnf(c_0_207,negated_conjecture,
and(t3,not(and(t1,and(t2,t3)))) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_193]),c_0_36]),c_0_194]) ).
cnf(c_0_208,negated_conjecture,
or(b,t1) = ll1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_195]),c_0_99]),c_0_99]),c_0_38]) ).
cnf(c_0_209,negated_conjecture,
not(carry) = and(t1,t5),
inference(spm,[status(thm)],[c_0_41,c_0_151]) ).
cnf(c_0_210,negated_conjecture,
or(t4,and(t2,X1)) = or(t4,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_141]),c_0_86]) ).
cnf(c_0_211,negated_conjecture,
and(t1,and(t5,carry)) = ll0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_151]),c_0_44]) ).
cnf(c_0_212,plain,
and(X1,and(X2,and(X1,or(X2,X3)))) = and(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_66]),c_0_44]) ).
cnf(c_0_213,negated_conjecture,
and(t3,or(b,t6)) = and(t3,t6),
inference(rw,[status(thm)],[c_0_196,c_0_197]) ).
cnf(c_0_214,negated_conjecture,
and(b,t3) = and(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_198]),c_0_96]),c_0_36]) ).
cnf(c_0_215,plain,
and(X1,and(X1,X2)) = and(X1,X2),
inference(spm,[status(thm)],[c_0_44,c_0_199]) ).
cnf(c_0_216,negated_conjecture,
or(t4,t6) = ll1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_200]),c_0_38]) ).
cnf(c_0_217,negated_conjecture,
or(and(t5,t4),and(t4,sum)) = and(t4,sum),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_49]),c_0_38]) ).
cnf(c_0_218,negated_conjecture,
and(t4,and(t6,t7)) = and(cin,t7),
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_39,c_0_201]),c_0_41]),c_0_72]),c_0_78]),c_0_44]),c_0_202]) ).
cnf(c_0_219,negated_conjecture,
and(t4,t7) = t4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_203,c_0_204]),c_0_77]) ).
cnf(c_0_220,negated_conjecture,
or(t1,and(a,X1)) = or(t1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_205]),c_0_86]) ).
cnf(c_0_221,negated_conjecture,
and(a,and(b,t4)) = ll0,
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_206,c_0_207]),c_0_36]),c_0_162]),c_0_94]),c_0_36]),c_0_136]) ).
cnf(c_0_222,negated_conjecture,
or(t1,and(b,X1)) = or(t1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_208]),c_0_86]) ).
cnf(c_0_223,negated_conjecture,
or(carry,and(t1,t5)) = ll1,
inference(spm,[status(thm)],[c_0_68,c_0_209]) ).
cnf(c_0_224,negated_conjecture,
or(t4,t3) = ll1,
inference(rw,[status(thm)],[c_0_127,c_0_210]) ).
cnf(c_0_225,negated_conjecture,
and(t1,or(X1,and(t5,carry))) = and(t1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_211]),c_0_80]) ).
cnf(c_0_226,negated_conjecture,
and(b,and(t3,t6)) = 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_212,c_0_213]),c_0_36]),c_0_214]),c_0_136]),c_0_215]) ).
cnf(c_0_227,negated_conjecture,
or(t4,and(t6,X1)) = or(t4,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_216]),c_0_86]) ).
cnf(c_0_228,negated_conjecture,
and(t6,and(t7,sum)) = ll0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_46]),c_0_44]) ).
cnf(c_0_229,negated_conjecture,
and(t4,or(t5,sum)) = and(t4,sum),
inference(rw,[status(thm)],[c_0_217,c_0_92]) ).
cnf(c_0_230,negated_conjecture,
and(cin,t7) = and(cin,t4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_218]),c_0_136]),c_0_219]) ).
cnf(c_0_231,negated_conjecture,
or(t1,t4) = t1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_221]),c_0_80]),c_0_222]) ).
cnf(c_0_232,negated_conjecture,
or(t1,carry) = ll1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_223]),c_0_99]),c_0_99]),c_0_38]) ).
cnf(c_0_233,negated_conjecture,
or(and(a,t1),and(t1,t4)) = and(t1,t4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_73]),c_0_38]) ).
cnf(c_0_234,negated_conjecture,
and(t4,or(X1,and(t2,t3))) = and(t4,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_191]),c_0_80]) ).
cnf(c_0_235,negated_conjecture,
or(b,and(X1,t3)) = or(b,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_139]),c_0_77]) ).
cnf(c_0_236,negated_conjecture,
or(t4,and(t3,X1)) = or(t4,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_224]),c_0_86]) ).
cnf(c_0_237,negated_conjecture,
and(t1,or(carry,t6)) = and(t1,t6),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_200]),c_0_38]) ).
cnf(c_0_238,negated_conjecture,
or(t6,and(a,b)) = t6,
inference(spm,[status(thm)],[c_0_56,c_0_226]) ).
cnf(c_0_239,axiom,
or(X1,X1) = X1,
or_idempotent ).
cnf(c_0_240,negated_conjecture,
or(and(cin,or(a,b)),and(not(cin),and(a,b))) = carry_def,
carry_def ).
cnf(c_0_241,negated_conjecture,
or(t4,and(t7,sum)) = t4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_227,c_0_228]),c_0_80]) ).
cnf(c_0_242,negated_conjecture,
and(t4,sum) = and(t5,t4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_229,c_0_201]),c_0_230]),c_0_60]),c_0_36]) ).
cnf(c_0_243,negated_conjecture,
and(t1,t4) = t4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_231]),c_0_36]) ).
cnf(c_0_244,negated_conjecture,
or(carry,and(t1,X1)) = or(carry,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_232]),c_0_86]) ).
cnf(c_0_245,negated_conjecture,
and(t1,or(a,t4)) = and(t1,t4),
inference(rw,[status(thm)],[c_0_233,c_0_92]) ).
cnf(c_0_246,plain,
or(X1,or(X2,X3)) = or(X3,or(X1,X2)),
inference(spm,[status(thm)],[c_0_38,c_0_69]) ).
cnf(c_0_247,negated_conjecture,
or(a,and(X1,t2)) = or(a,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_116]),c_0_77]) ).
cnf(c_0_248,negated_conjecture,
and(t4,t2) = and(b,t4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_235]),c_0_135]),c_0_36]) ).
cnf(c_0_249,negated_conjecture,
or(t4,and(b,t1)) = t4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_236,c_0_87]),c_0_80]),c_0_138]) ).
cnf(c_0_250,negated_conjecture,
and(t1,and(carry,t6)) = and(t1,carry),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_237]),c_0_136]),c_0_215]) ).
cnf(c_0_251,negated_conjecture,
and(a,and(b,t6)) = and(a,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_238]),c_0_44]) ).
cnf(c_0_252,negated_conjecture,
or(t1,and(X1,b)) = or(t1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_208]),c_0_77]) ).
cnf(c_0_253,plain,
and(X1,and(X2,or(and(X1,X2),X3))) = and(X1,X2),
inference(spm,[status(thm)],[c_0_37,c_0_44]) ).
cnf(c_0_254,plain,
or(X1,or(X1,X2)) = or(X1,X2),
inference(spm,[status(thm)],[c_0_69,c_0_239]) ).
cnf(c_0_255,negated_conjecture,
or(and(a,and(b,not(cin))),and(cin,or(a,b))) = carry_def,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_240,c_0_36]),c_0_44]),c_0_38]) ).
cnf(c_0_256,negated_conjecture,
and(t6,or(X1,and(t7,sum))) = and(t6,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_228]),c_0_80]) ).
cnf(c_0_257,negated_conjecture,
and(t7,sum) = and(t5,t4),
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_43,c_0_241]),c_0_44]),c_0_36]),c_0_242]),c_0_94]),c_0_36]),c_0_136]),c_0_219]) ).
cnf(c_0_258,negated_conjecture,
or(carry,and(t1,and(t5,X1))) = or(carry,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_223]),c_0_44]),c_0_86]) ).
cnf(c_0_259,negated_conjecture,
or(a,and(t1,X1)) = or(a,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_205]),c_0_86]) ).
cnf(c_0_260,negated_conjecture,
and(t1,or(t4,carry)) = t4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_143]),c_0_243]) ).
cnf(c_0_261,negated_conjecture,
or(a,or(t4,carry)) = or(t4,carry),
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_244,c_0_245]),c_0_244]),c_0_38]),c_0_246]),c_0_38]),c_0_145]) ).
cnf(c_0_262,negated_conjecture,
or(a,and(b,t4)) = or(a,t4),
inference(spm,[status(thm)],[c_0_247,c_0_248]) ).
cnf(c_0_263,negated_conjecture,
and(b,t4) = and(b,t1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_249]),c_0_44]),c_0_243]) ).
cnf(c_0_264,negated_conjecture,
or(a,and(X1,t1)) = or(a,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_205]),c_0_77]) ).
cnf(c_0_265,negated_conjecture,
and(carry,or(t1,t6)) = and(carry,t6),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_250]),c_0_188]),c_0_38]) ).
cnf(c_0_266,negated_conjecture,
or(t1,t6) = ll1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_251]),c_0_252]),c_0_38]),c_0_205]),c_0_222]) ).
cnf(c_0_267,plain,
and(X1,and(not(X1),X2)) = ll0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_253,c_0_87]),c_0_90]) ).
cnf(c_0_268,negated_conjecture,
or(carry_def,and(a,and(b,not(cin)))) = carry_def,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_254,c_0_255]),c_0_38]) ).
cnf(c_0_269,negated_conjecture,
and(t6,or(X1,and(t5,t4))) = and(t6,X1),
inference(rw,[status(thm)],[c_0_256,c_0_257]) ).
cnf(c_0_270,negated_conjecture,
or(carry,and(t5,X1)) = or(carry,X1),
inference(rw,[status(thm)],[c_0_258,c_0_244]) ).
cnf(c_0_271,negated_conjecture,
or(t4,carry) = or(a,t4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_259,c_0_260]),c_0_261]) ).
cnf(c_0_272,negated_conjecture,
or(a,t4) = or(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_262,c_0_263]),c_0_264]) ).
cnf(c_0_273,negated_conjecture,
and(carry,t6) = carry,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_265,c_0_266]),c_0_77]) ).
cnf(c_0_274,plain,
and(X1,and(X2,not(X1))) = ll0,
inference(spm,[status(thm)],[c_0_267,c_0_36]) ).
cnf(c_0_275,negated_conjecture,
and(not(carry_def),not(and(a,and(b,not(cin))))) = not(carry_def),
inference(spm,[status(thm)],[c_0_39,c_0_268]) ).
cnf(c_0_276,negated_conjecture,
and(t6,or(a,b)) = carry,
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_269,c_0_270]),c_0_38]),c_0_271]),c_0_272]),c_0_36]),c_0_273]) ).
cnf(c_0_277,negated_conjecture,
and(a,and(b,and(not(cin),not(carry_def)))) = ll0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_274,c_0_275]),c_0_44]),c_0_44]) ).
cnf(c_0_278,plain,
or(X1,or(and(X1,X2),X3)) = or(X1,X3),
inference(spm,[status(thm)],[c_0_69,c_0_40]) ).
cnf(c_0_279,negated_conjecture,
or(carry_def,and(cin,or(a,b))) = carry_def,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_255]),c_0_38]),c_0_255]),c_0_38]) ).
cnf(c_0_280,negated_conjecture,
and(cin,or(a,b)) = and(cin,carry),
inference(spm,[status(thm)],[c_0_185,c_0_276]) ).
cnf(c_0_281,negated_conjecture,
or(t1,and(not(cin),not(carry_def))) = t1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_277]),c_0_80]),c_0_222]) ).
cnf(c_0_282,negated_conjecture,
or(a,and(cin,or(a,b))) = or(a,carry_def),
inference(spm,[status(thm)],[c_0_278,c_0_255]) ).
cnf(c_0_283,negated_conjecture,
or(carry_def,and(cin,carry)) = carry_def,
inference(rw,[status(thm)],[c_0_279,c_0_280]) ).
cnf(c_0_284,negated_conjecture,
and(a,and(b,or(cin,carry_def))) = 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_39,c_0_281]),c_0_84]),c_0_84]),c_0_82]),c_0_44]) ).
cnf(c_0_285,negated_conjecture,
or(a,or(cin,carry_def)) = or(a,cin),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_282]),c_0_145]),c_0_254]) ).
cnf(c_0_286,negated_conjecture,
and(cin,and(carry,carry_def)) = and(cin,carry),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_283]),c_0_44]) ).
cnf(c_0_287,negated_conjecture,
and(b,or(cin,carry_def)) = and(b,or(a,cin)),
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_51,c_0_284]),c_0_188]),c_0_69]),c_0_38]),c_0_145]),c_0_285]) ).
cnf(c_0_288,negated_conjecture,
xor(xor(a,b),cin) = sum_def,
sum_def ).
cnf(c_0_289,axiom,
or(and(not(X1),X2),and(X1,not(X2))) = xor(X1,X2),
xor_definition ).
cnf(c_0_290,negated_conjecture,
or(t1,and(carry,X1)) = or(t1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_232]),c_0_86]) ).
cnf(c_0_291,negated_conjecture,
and(carry,or(cin,carry_def)) = and(carry,carry_def),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_286]),c_0_188]),c_0_38]) ).
cnf(c_0_292,negated_conjecture,
or(cin,or(t1,carry_def)) = ll1,
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_222,c_0_287]),c_0_222]),c_0_246]),c_0_38]),c_0_205]),c_0_99]),c_0_145]) ).
cnf(c_0_293,negated_conjecture,
or(t5,carry) = ll1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_258,c_0_199]),c_0_223]),c_0_38]) ).
cnf(c_0_294,negated_conjecture,
or(and(not(or(and(not(a),b),and(a,not(b)))),cin),and(or(and(not(a),b),and(a,not(b))),not(cin))) = sum_def,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_288,c_0_289]),c_0_289]) ).
cnf(c_0_295,negated_conjecture,
or(t1,carry_def) = ll1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_290,c_0_291]),c_0_290]),c_0_145]),c_0_292]) ).
cnf(c_0_296,negated_conjecture,
or(t5,and(cin,X1)) = or(t5,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_85]),c_0_86]) ).
cnf(c_0_297,negated_conjecture,
or(t5,and(carry,X1)) = or(t5,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_293]),c_0_86]) ).
cnf(c_0_298,negated_conjecture,
or(and(and(not(and(not(a),b)),not(and(a,not(b)))),cin),and(or(and(not(a),b),and(a,not(b))),not(cin))) = sum_def,
inference(rw,[status(thm)],[c_0_294,c_0_39]) ).
cnf(c_0_299,axiom,
xor(X1,xor(X2,X3)) = xor(xor(X1,X2),X3),
xor_associative ).
cnf(c_0_300,negated_conjecture,
or(cin,and(t4,sum)) = or(cin,t4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_49]),c_0_100]) ).
cnf(c_0_301,negated_conjecture,
or(sum,and(t6,not(cin))) = not(and(cin,and(t6,t7))),
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_102,c_0_134]),c_0_93]),c_0_78]),c_0_44]),c_0_36]),c_0_136]) ).
cnf(c_0_302,negated_conjecture,
and(a,and(b,not(carry_def))) = ll0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_295]),c_0_158]),c_0_84]),c_0_44]) ).
cnf(c_0_303,negated_conjecture,
or(t5,carry_def) = ll1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_296,c_0_286]),c_0_296]),c_0_293]),c_0_297]) ).
cnf(c_0_304,negated_conjecture,
or(and(not(cin),or(and(a,not(b)),and(b,not(a)))),and(not(and(a,not(b))),and(cin,not(and(b,not(a)))))) = sum_def,
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_298,c_0_38]),c_0_38]),c_0_36]),c_0_36]),c_0_36]),c_0_36]),c_0_44]),c_0_36]) ).
cnf(c_0_305,plain,
or(and(not(X1),or(and(not(X2),X3),and(X2,not(X3)))),and(X1,not(or(and(not(X2),X3),and(X2,not(X3)))))) = or(and(not(or(and(not(X1),X2),and(X1,not(X2)))),X3),and(or(and(not(X1),X2),and(X1,not(X2))),not(X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_299,c_0_289]),c_0_289]),c_0_289]),c_0_289]) ).
cnf(c_0_306,negated_conjecture,
and(not(cin),not(and(t4,sum))) = and(t2,and(t3,not(cin))),
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_39,c_0_300]),c_0_39]),c_0_53]),c_0_94]),c_0_36]),c_0_136]) ).
cnf(c_0_307,negated_conjecture,
and(sum,not(and(cin,and(t6,t7)))) = sum,
inference(spm,[status(thm)],[c_0_37,c_0_301]) ).
cnf(c_0_308,negated_conjecture,
not(and(a,and(b,carry_def))) = t1,
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_220,c_0_302]),c_0_80]),c_0_222]),c_0_93]),c_0_84]),c_0_44]) ).
cnf(c_0_309,negated_conjecture,
and(cin,and(t4,not(carry_def))) = ll0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_303]),c_0_158]),c_0_72]),c_0_44]) ).
cnf(c_0_310,negated_conjecture,
or(t5,and(t4,X1)) = or(t5,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_131]),c_0_86]) ).
cnf(c_0_311,negated_conjecture,
or(and(cin,and(not(and(a,not(b))),not(and(b,not(a))))),and(not(cin),or(and(a,not(b)),and(b,not(a))))) = sum_def,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_304,c_0_94]),c_0_36]),c_0_38]) ).
cnf(c_0_312,plain,
or(and(X1,and(not(and(X2,not(X3))),not(and(not(X2),X3)))),and(not(X1),or(and(X2,not(X3)),and(not(X2),X3)))) = or(and(not(and(X1,not(X2))),and(not(and(not(X1),X2)),X3)),and(or(and(X1,not(X2)),and(not(X1),X2)),not(X3))),
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_305,c_0_38]),c_0_38]),c_0_39]),c_0_38]),c_0_38]),c_0_39]),c_0_44]),c_0_38]) ).
cnf(c_0_313,axiom,
not(ll0) = ll1,
ll0_inverse ).
cnf(c_0_314,negated_conjecture,
and(not(a),not(b)) = and(t1,and(t2,t3)),
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_39,c_0_272]),c_0_39]),c_0_53]),c_0_94]),c_0_36]),c_0_175]),c_0_193]) ).
cnf(c_0_315,negated_conjecture,
and(t1,or(a,t4)) = t4,
inference(rw,[status(thm)],[c_0_245,c_0_243]) ).
cnf(c_0_316,negated_conjecture,
and(t2,and(t3,not(cin))) = and(t5,and(t6,t7)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_306,c_0_242]),c_0_42]),c_0_36]),c_0_183]) ).
cnf(c_0_317,negated_conjecture,
and(sum,not(and(cin,t7))) = sum,
inference(rw,[status(thm)],[c_0_307,c_0_185]) ).
cnf(c_0_318,negated_conjecture,
or(cin,and(t7,X1)) = or(cin,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_173]),c_0_86]) ).
cnf(c_0_319,negated_conjecture,
and(not(and(a,and(b,not(cin)))),not(and(cin,or(a,b)))) = not(carry_def),
inference(spm,[status(thm)],[c_0_39,c_0_255]) ).
cnf(c_0_320,negated_conjecture,
and(a,and(b,carry_def)) = and(a,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_308]),c_0_84]) ).
cnf(c_0_321,negated_conjecture,
not(and(cin,and(t4,carry_def))) = t5,
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_296,c_0_309]),c_0_80]),c_0_310]),c_0_93]),c_0_72]),c_0_44]) ).
cnf(c_0_322,negated_conjecture,
or(and(cin,and(t2,not(and(b,not(a))))),and(not(cin),or(and(a,t1),and(b,not(a))))) = sum_def,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_311,c_0_149]),c_0_62]),c_0_149]) ).
cnf(c_0_323,plain,
and(not(and(X1,not(X2))),not(and(not(X1),X2))) = or(and(X1,X2),and(not(X1),not(X2))),
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(spm,[status(thm)],[c_0_312,c_0_158]),c_0_103]),c_0_313]),c_0_77]),c_0_41]),c_0_86]),c_0_103]),c_0_77]),c_0_90]),c_0_77]),c_0_103]),c_0_80]) ).
cnf(c_0_324,negated_conjecture,
not(and(t1,and(t2,t3))) = or(a,b),
inference(spm,[status(thm)],[c_0_82,c_0_314]) ).
cnf(c_0_325,negated_conjecture,
and(t1,or(a,b)) = t4,
inference(rw,[status(thm)],[c_0_315,c_0_272]) ).
cnf(c_0_326,negated_conjecture,
or(t4,and(t6,t7)) = not(and(cin,and(t2,t3))),
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_210,c_0_316]),c_0_143]),c_0_236]),c_0_93]),c_0_53]),c_0_44]),c_0_36]),c_0_136]) ).
cnf(c_0_327,negated_conjecture,
or(t4,t7) = t7,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_219]),c_0_38]) ).
cnf(c_0_328,negated_conjecture,
and(t5,sum) = sum,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_317,c_0_230]),c_0_60]),c_0_36]) ).
cnf(c_0_329,negated_conjecture,
and(t6,or(cin,sum)) = cin,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_256,c_0_318]),c_0_36]),c_0_133]) ).
cnf(c_0_330,negated_conjecture,
and(not(and(cin,carry)),not(and(a,and(b,not(cin))))) = not(carry_def),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_319,c_0_280]),c_0_36]) ).
cnf(c_0_331,negated_conjecture,
not(and(a,and(b,not(X1)))) = or(X1,t1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_84]),c_0_94]),c_0_36]),c_0_136]) ).
cnf(c_0_332,negated_conjecture,
or(carry_def,and(a,b)) = carry_def,
inference(spm,[status(thm)],[c_0_56,c_0_320]) ).
cnf(c_0_333,negated_conjecture,
and(not(carry_def),not(and(cin,or(a,b)))) = not(carry_def),
inference(spm,[status(thm)],[c_0_39,c_0_279]) ).
cnf(c_0_334,negated_conjecture,
and(cin,and(t4,carry_def)) = and(cin,t4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_321]),c_0_72]) ).
cnf(c_0_335,negated_conjecture,
or(and(cin,and(t2,t3)),and(not(cin),or(and(a,t1),and(b,t1)))) = sum_def,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_322,c_0_198]),c_0_96]),c_0_198]) ).
cnf(c_0_336,negated_conjecture,
or(and(a,t1),and(b,t1)) = t4,
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_323,c_0_314]),c_0_41]),c_0_74]),c_0_324]),c_0_325]),c_0_149]),c_0_41]),c_0_36]),c_0_198]) ).
cnf(c_0_337,negated_conjecture,
not(and(cin,and(t2,t3))) = t7,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_326,c_0_227]),c_0_327]) ).
cnf(c_0_338,negated_conjecture,
and(t5,or(cin,sum)) = sum,
inference(rw,[status(thm)],[c_0_144,c_0_328]) ).
cnf(c_0_339,negated_conjecture,
or(cin,sum) = or(cin,t4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_227,c_0_329]),c_0_38]),c_0_145]),c_0_157]),c_0_254]) ).
cnf(c_0_340,plain,
and(X1,and(X2,and(X1,or(X3,X2)))) = and(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_66]),c_0_44]) ).
cnf(c_0_341,negated_conjecture,
and(not(and(cin,carry)),or(cin,t1)) = not(carry_def),
inference(rw,[status(thm)],[c_0_330,c_0_331]) ).
cnf(c_0_342,negated_conjecture,
and(t1,not(carry_def)) = not(carry_def),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_332]),c_0_74]),c_0_36]) ).
cnf(c_0_343,negated_conjecture,
and(not(carry_def),not(and(cin,carry))) = not(carry_def),
inference(rw,[status(thm)],[c_0_333,c_0_280]) ).
cnf(c_0_344,negated_conjecture,
and(t1,or(cin,carry)) = and(cin,t1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_100]),c_0_36]) ).
cnf(c_0_345,negated_conjecture,
or(carry_def,and(cin,t4)) = carry_def,
inference(spm,[status(thm)],[c_0_56,c_0_334]) ).
cnf(c_0_346,negated_conjecture,
or(and(t5,t4),and(cin,and(t2,t3))) = sum_def,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_335,c_0_336]),c_0_36]),c_0_159]),c_0_38]) ).
cnf(c_0_347,negated_conjecture,
and(cin,and(t2,t3)) = and(cin,t5),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_337]),c_0_104]) ).
cnf(c_0_348,negated_conjecture,
and(t5,or(cin,t4)) = sum,
inference(rw,[status(thm)],[c_0_338,c_0_339]) ).
cnf(c_0_349,negated_conjecture,
and(t1,not(and(cin,carry))) = not(carry_def),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_340,c_0_341]),c_0_342]),c_0_36]),c_0_343]),c_0_36]) ).
cnf(c_0_350,negated_conjecture,
and(cin,and(t1,carry)) = and(t1,carry),
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_340,c_0_344]),c_0_94]),c_0_36]),c_0_136]),c_0_136]),c_0_215]) ).
cnf(c_0_351,negated_conjecture,
not(and(t1,and(t5,not(X1)))) = or(X1,carry),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_209]),c_0_94]),c_0_36]),c_0_136]) ).
cnf(c_0_352,negated_conjecture,
and(t5,not(carry_def)) = not(carry_def),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_345]),c_0_60]),c_0_36]) ).
cnf(c_0_353,negated_conjecture,
( sum != sum_def
| carry != carry_def ),
prove_circuit ).
cnf(c_0_354,negated_conjecture,
sum_def = sum,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_346,c_0_347]),c_0_188]),c_0_38]),c_0_348]) ).
cnf(c_0_355,negated_conjecture,
and(t1,carry_def) = and(t1,carry),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_349]),c_0_41]),c_0_136]),c_0_350]) ).
cnf(c_0_356,negated_conjecture,
or(carry,carry_def) = carry_def,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_351,c_0_352]),c_0_342]),c_0_41]),c_0_38]) ).
cnf(c_0_357,negated_conjecture,
carry_def != carry,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_353,c_0_354])]) ).
cnf(c_0_358,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244,c_0_355]),c_0_244]),c_0_239]),c_0_356]),c_0_357]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HWV003-2 : TPTP v9.2.1. Released v2.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.17/0.33 % Computer : n014.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 19:10:36 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 11.07/7.33 % Version : CSE_E---1.7
% 11.07/7.33 % Problem : theBenchmark.p
% 11.07/7.33 % SZS status Unsatisfiable for theBenchmark.p
% 11.07/7.33 % SZS output start CNFRefutation
% See solution above
% 11.07/7.37 % Total time : 5.372s
%------------------------------------------------------------------------------