TSTP Solution File: HWV003-2 by E---3.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : HWV003-2 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n001.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 17:51:07 EDT 2023
% Result : Unsatisfiable 8.46s 1.60s
% Output : CNFRefutation 8.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 36
% Syntax : Number of clauses : 345 ( 343 unt; 0 nHn; 227 RR)
% Number of literals : 347 ( 346 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 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 : 213 ( 27 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t5,negated_conjecture,
not(and(t4,cin)) = t5,
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',t5) ).
cnf(and_commutative,axiom,
and(X1,X2) = and(X2,X1),
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',and_commutative) ).
cnf(xor_definition,axiom,
or(and(not(X1),X2),and(X1,not(X2))) = xor(X1,X2),
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',xor_definition) ).
cnf(or_commutative,axiom,
or(X1,X2) = or(X2,X1),
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',or_commutative) ).
cnf(t6,negated_conjecture,
not(and(t4,t5)) = t6,
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',t6) ).
cnf(or_demorgan,axiom,
not(or(X1,X2)) = and(not(X1),not(X2)),
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',or_demorgan) ).
cnf(or_absorption,axiom,
or(X1,and(X1,X2)) = X1,
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',or_absorption) ).
cnf(not_involution,axiom,
not(not(X1)) = X1,
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',not_involution) ).
cnf(and_boundedness,axiom,
and(X1,ll0) = ll0,
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',and_boundedness) ).
cnf(ll0_inverse,axiom,
not(ll0) = ll1,
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',ll0_inverse) ).
cnf(and_identity,axiom,
and(X1,ll1) = X1,
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',and_identity) ).
cnf(or_identity,axiom,
or(X1,ll0) = X1,
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',or_identity) ).
cnf(t7,negated_conjecture,
not(and(t5,cin)) = t7,
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',t7) ).
cnf(and_associative,axiom,
and(and(X1,X2),X3) = and(X1,and(X2,X3)),
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',and_associative) ).
cnf(and_absorption,axiom,
and(X1,or(X1,X2)) = X1,
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',and_absorption) ).
cnf(and_complement,axiom,
and(X1,not(X1)) = ll0,
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',and_complement) ).
cnf(or_idempotent,axiom,
or(X1,X1) = X1,
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',or_idempotent) ).
cnf(xor_commutative,axiom,
xor(X1,X2) = xor(X2,X1),
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',xor_commutative) ).
cnf(t1,negated_conjecture,
not(and(a,b)) = t1,
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',t1) ).
cnf(and_idempotent,axiom,
and(X1,X1) = X1,
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',and_idempotent) ).
cnf(and_demorgan,axiom,
not(and(X1,X2)) = or(not(X1),not(X2)),
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',and_demorgan) ).
cnf(t2,negated_conjecture,
not(and(a,t1)) = t2,
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',t2) ).
cnf(sum,negated_conjecture,
not(and(t6,t7)) = sum,
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',sum) ).
cnf(xor_associative,axiom,
xor(X1,xor(X2,X3)) = xor(xor(X1,X2),X3),
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',xor_associative) ).
cnf(ll1_inverse,axiom,
not(ll1) = ll0,
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',ll1_inverse) ).
cnf(or_complement,axiom,
or(X1,not(X1)) = ll1,
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',or_complement) ).
cnf(and_distributive,axiom,
or(X1,and(X2,X3)) = and(or(X1,X2),or(X1,X3)),
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',and_distributive) ).
cnf(or_associative,axiom,
or(or(X1,X2),X3) = or(X1,or(X2,X3)),
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',or_associative) ).
cnf(or_distributive,axiom,
and(X1,or(X2,X3)) = or(and(X1,X2),and(X1,X3)),
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',or_distributive) ).
cnf(or_boundedness,axiom,
or(X1,ll1) = ll1,
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',or_boundedness) ).
cnf(t4,negated_conjecture,
not(and(t2,t3)) = t4,
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',t4) ).
cnf(t3,negated_conjecture,
not(and(b,t1)) = t3,
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',t3) ).
cnf(carry,negated_conjecture,
not(and(t1,t5)) = carry,
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',carry) ).
cnf(carry_def,negated_conjecture,
or(and(cin,or(a,b)),and(not(cin),and(a,b))) = carry_def,
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',carry_def) ).
cnf(sum_def,negated_conjecture,
xor(xor(a,b),cin) = sum_def,
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',sum_def) ).
cnf(prove_circuit,negated_conjecture,
( sum != sum_def
| carry != carry_def ),
file('/export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p',prove_circuit) ).
cnf(c_0_36,negated_conjecture,
not(and(t4,cin)) = t5,
t5 ).
cnf(c_0_37,axiom,
and(X1,X2) = and(X2,X1),
and_commutative ).
cnf(c_0_38,axiom,
or(and(not(X1),X2),and(X1,not(X2))) = xor(X1,X2),
xor_definition ).
cnf(c_0_39,axiom,
or(X1,X2) = or(X2,X1),
or_commutative ).
cnf(c_0_40,negated_conjecture,
not(and(t4,t5)) = t6,
t6 ).
cnf(c_0_41,axiom,
not(or(X1,X2)) = and(not(X1),not(X2)),
or_demorgan ).
cnf(c_0_42,axiom,
or(X1,and(X1,X2)) = X1,
or_absorption ).
cnf(c_0_43,axiom,
not(not(X1)) = X1,
not_involution ).
cnf(c_0_44,negated_conjecture,
not(and(cin,t4)) = t5,
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,plain,
or(and(X1,not(X2)),and(not(X1),X2)) = xor(X1,X2),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,axiom,
and(X1,ll0) = ll0,
and_boundedness ).
cnf(c_0_47,axiom,
not(ll0) = ll1,
ll0_inverse ).
cnf(c_0_48,axiom,
and(X1,ll1) = X1,
and_identity ).
cnf(c_0_49,axiom,
or(X1,ll0) = X1,
or_identity ).
cnf(c_0_50,negated_conjecture,
not(and(t5,t4)) = t6,
inference(rw,[status(thm)],[c_0_40,c_0_37]) ).
cnf(c_0_51,negated_conjecture,
not(and(t5,cin)) = t7,
t7 ).
cnf(c_0_52,plain,
and(not(X1),not(and(X1,X2))) = not(X1),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_53,negated_conjecture,
not(t5) = and(cin,t4),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_54,axiom,
and(and(X1,X2),X3) = and(X1,and(X2,X3)),
and_associative ).
cnf(c_0_55,axiom,
and(X1,or(X1,X2)) = X1,
and_absorption ).
cnf(c_0_56,axiom,
and(X1,not(X1)) = ll0,
and_complement ).
cnf(c_0_57,axiom,
or(X1,X1) = X1,
or_idempotent ).
cnf(c_0_58,axiom,
xor(X1,X2) = xor(X2,X1),
xor_commutative ).
cnf(c_0_59,plain,
xor(X1,ll0) = X1,
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_48]),c_0_49]) ).
cnf(c_0_60,negated_conjecture,
not(and(a,b)) = t1,
t1 ).
cnf(c_0_61,axiom,
and(X1,X1) = X1,
and_idempotent ).
cnf(c_0_62,axiom,
not(and(X1,X2)) = or(not(X1),not(X2)),
and_demorgan ).
cnf(c_0_63,negated_conjecture,
not(and(a,t1)) = t2,
t2 ).
cnf(c_0_64,negated_conjecture,
not(and(t6,t7)) = sum,
sum ).
cnf(c_0_65,negated_conjecture,
not(t6) = and(t5,t4),
inference(spm,[status(thm)],[c_0_43,c_0_50]) ).
cnf(c_0_66,negated_conjecture,
not(and(cin,t5)) = t7,
inference(rw,[status(thm)],[c_0_51,c_0_37]) ).
cnf(c_0_67,plain,
or(X1,and(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_42,c_0_37]) ).
cnf(c_0_68,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_52,c_0_50]),c_0_53]),c_0_54]),c_0_53]) ).
cnf(c_0_69,plain,
and(X1,or(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_55,c_0_39]) ).
cnf(c_0_70,axiom,
xor(X1,xor(X2,X3)) = xor(xor(X1,X2),X3),
xor_associative ).
cnf(c_0_71,plain,
xor(X1,X1) = ll0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_56]),c_0_43]),c_0_56]),c_0_57]),c_0_43]) ).
cnf(c_0_72,plain,
xor(ll0,X1) = X1,
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_73,negated_conjecture,
and(t1,not(a)) = not(a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_60]),c_0_37]) ).
cnf(c_0_74,negated_conjecture,
not(t1) = and(a,b),
inference(spm,[status(thm)],[c_0_43,c_0_60]) ).
cnf(c_0_75,plain,
and(X1,and(X1,X2)) = and(X1,X2),
inference(spm,[status(thm)],[c_0_54,c_0_61]) ).
cnf(c_0_76,plain,
or(not(X1),X2) = not(and(X1,not(X2))),
inference(spm,[status(thm)],[c_0_62,c_0_43]) ).
cnf(c_0_77,negated_conjecture,
and(t2,not(a)) = not(a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_63]),c_0_37]) ).
cnf(c_0_78,negated_conjecture,
not(t2) = and(a,t1),
inference(spm,[status(thm)],[c_0_43,c_0_63]) ).
cnf(c_0_79,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_52,c_0_64]),c_0_65]),c_0_54]),c_0_65]) ).
cnf(c_0_80,negated_conjecture,
and(t5,not(cin)) = not(cin),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_44]),c_0_37]) ).
cnf(c_0_81,negated_conjecture,
and(t7,not(cin)) = not(cin),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_66]),c_0_37]) ).
cnf(c_0_82,negated_conjecture,
not(t7) = and(cin,t5),
inference(spm,[status(thm)],[c_0_43,c_0_66]) ).
cnf(c_0_83,negated_conjecture,
or(and(cin,t4),and(t4,t6)) = and(t4,t6),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_39]) ).
cnf(c_0_84,plain,
and(X1,and(X2,X1)) = and(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_42]),c_0_54]) ).
cnf(c_0_85,negated_conjecture,
and(t5,and(t4,t6)) = ll0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_50]),c_0_54]) ).
cnf(c_0_86,plain,
xor(X1,xor(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]) ).
cnf(c_0_87,negated_conjecture,
xor(a,t1) = t2,
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_45,c_0_73]),c_0_74]),c_0_54]),c_0_37]),c_0_75]),c_0_76]),c_0_60]),c_0_63]),c_0_58]) ).
cnf(c_0_88,negated_conjecture,
xor(a,t2) = not(and(a,t2)),
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_45,c_0_77]),c_0_78]),c_0_54]),c_0_37]),c_0_75]),c_0_76]),c_0_63]),c_0_58]) ).
cnf(c_0_89,negated_conjecture,
or(and(t5,t4),and(t4,sum)) = and(t4,sum),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_79]),c_0_39]) ).
cnf(c_0_90,axiom,
not(ll1) = ll0,
ll1_inverse ).
cnf(c_0_91,plain,
or(ll0,X1) = X1,
inference(spm,[status(thm)],[c_0_49,c_0_39]) ).
cnf(c_0_92,axiom,
or(X1,not(X1)) = ll1,
or_complement ).
cnf(c_0_93,negated_conjecture,
not(sum) = and(t6,t7),
inference(spm,[status(thm)],[c_0_43,c_0_64]) ).
cnf(c_0_94,negated_conjecture,
xor(cin,t5) = 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_45,c_0_80]),c_0_53]),c_0_54]),c_0_37]),c_0_75]),c_0_76]),c_0_44]),c_0_66]),c_0_58]) ).
cnf(c_0_95,negated_conjecture,
xor(cin,t7) = 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(spm,[status(thm)],[c_0_45,c_0_81]),c_0_82]),c_0_54]),c_0_37]),c_0_75]),c_0_76]),c_0_66]),c_0_58]) ).
cnf(c_0_96,negated_conjecture,
and(t5,not(and(t4,t6))) = not(and(t4,t6)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_83]),c_0_44]) ).
cnf(c_0_97,negated_conjecture,
and(t4,and(t5,t6)) = ll0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_46]),c_0_54]),c_0_37]) ).
cnf(c_0_98,negated_conjecture,
not(and(a,t2)) = t1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88]) ).
cnf(c_0_99,negated_conjecture,
and(t6,not(and(t4,sum))) = not(and(t4,sum)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_89]),c_0_50]) ).
cnf(c_0_100,plain,
xor(X1,ll1) = not(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_48]),c_0_90]),c_0_46]),c_0_91]) ).
cnf(c_0_101,axiom,
or(X1,and(X2,X3)) = and(or(X1,X2),or(X1,X3)),
and_distributive ).
cnf(c_0_102,negated_conjecture,
or(sum,and(t6,t7)) = ll1,
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_103,plain,
and(ll1,X1) = X1,
inference(spm,[status(thm)],[c_0_48,c_0_37]) ).
cnf(c_0_104,plain,
not(and(not(X1),not(X2))) = or(X1,X2),
inference(spm,[status(thm)],[c_0_43,c_0_41]) ).
cnf(c_0_105,negated_conjecture,
not(and(cin,t7)) = t5,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_94]),c_0_95]) ).
cnf(c_0_106,negated_conjecture,
xor(t5,and(t4,t6)) = 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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_96]),c_0_53]),c_0_54]),c_0_75]),c_0_68]),c_0_76]),c_0_44]),c_0_54]),c_0_37]),c_0_97]),c_0_47]) ).
cnf(c_0_107,negated_conjecture,
and(a,t2) = and(a,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_98]),c_0_74]) ).
cnf(c_0_108,plain,
xor(X1,xor(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_86,c_0_58]) ).
cnf(c_0_109,negated_conjecture,
xor(t6,and(t4,sum)) = not(and(t4,and(t6,sum))),
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_45,c_0_99]),c_0_65]),c_0_54]),c_0_75]),c_0_79]),c_0_76]),c_0_50]),c_0_54]),c_0_37]) ).
cnf(c_0_110,plain,
xor(X1,not(X2)) = not(xor(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_100]),c_0_100]) ).
cnf(c_0_111,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_101,c_0_102]),c_0_54]),c_0_103]) ).
cnf(c_0_112,plain,
or(X1,not(X2)) = not(and(not(X1),X2)),
inference(spm,[status(thm)],[c_0_104,c_0_43]) ).
cnf(c_0_113,negated_conjecture,
and(cin,t7) = and(cin,t4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_105]),c_0_53]) ).
cnf(c_0_114,plain,
and(X1,and(X2,X3)) = and(X3,and(X1,X2)),
inference(spm,[status(thm)],[c_0_37,c_0_54]) ).
cnf(c_0_115,negated_conjecture,
and(t4,t6) = and(cin,t4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_106]),c_0_100]),c_0_53]) ).
cnf(c_0_116,negated_conjecture,
or(t2,and(a,b)) = t2,
inference(spm,[status(thm)],[c_0_67,c_0_107]) ).
cnf(c_0_117,axiom,
or(or(X1,X2),X3) = or(X1,or(X2,X3)),
or_associative ).
cnf(c_0_118,negated_conjecture,
not(xor(and(t4,sum),and(t4,and(t6,sum)))) = t6,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_110]) ).
cnf(c_0_119,plain,
and(X1,and(X2,not(and(X1,X2)))) = ll0,
inference(spm,[status(thm)],[c_0_56,c_0_54]) ).
cnf(c_0_120,negated_conjecture,
or(sum,and(t6,not(cin))) = t5,
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_111,c_0_81]),c_0_112]),c_0_93]),c_0_54]),c_0_37]),c_0_113]),c_0_114]),c_0_115]),c_0_75]),c_0_44]) ).
cnf(c_0_121,negated_conjecture,
and(a,and(b,t2)) = and(a,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_116]),c_0_54]) ).
cnf(c_0_122,axiom,
and(X1,or(X2,X3)) = or(and(X1,X2),and(X1,X3)),
or_distributive ).
cnf(c_0_123,plain,
or(X1,or(X2,or(X1,and(X2,X3)))) = or(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_101]),c_0_117]) ).
cnf(c_0_124,negated_conjecture,
or(t2,and(a,t1)) = ll1,
inference(spm,[status(thm)],[c_0_92,c_0_78]) ).
cnf(c_0_125,axiom,
or(X1,ll1) = ll1,
or_boundedness ).
cnf(c_0_126,negated_conjecture,
xor(and(t4,sum),and(t4,and(t6,sum))) = and(t5,t4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_118]),c_0_65]) ).
cnf(c_0_127,negated_conjecture,
and(t5,and(t4,and(t6,sum))) = ll0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_79]),c_0_50]),c_0_54]),c_0_37]) ).
cnf(c_0_128,negated_conjecture,
and(t5,sum) = sum,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_120]),c_0_37]) ).
cnf(c_0_129,negated_conjecture,
or(and(a,b),and(b,t2)) = and(b,t2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_121]),c_0_39]) ).
cnf(c_0_130,plain,
or(and(X1,X2),and(X2,X3)) = and(X2,or(X1,X3)),
inference(spm,[status(thm)],[c_0_122,c_0_37]) ).
cnf(c_0_131,negated_conjecture,
or(a,t2) = ll1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_125]),c_0_125]),c_0_39]) ).
cnf(c_0_132,plain,
and(X1,and(X2,or(and(X1,X2),X3))) = and(X1,X2),
inference(spm,[status(thm)],[c_0_55,c_0_54]) ).
cnf(c_0_133,negated_conjecture,
xor(and(t5,t4),and(t4,and(t6,sum))) = and(t4,sum),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_126]),c_0_58]) ).
cnf(c_0_134,negated_conjecture,
and(t4,and(t6,sum)) = 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_84,c_0_127]),c_0_46]),c_0_54]),c_0_54]),c_0_37]),c_0_128]) ).
cnf(c_0_135,negated_conjecture,
not(and(t2,t3)) = t4,
t4 ).
cnf(c_0_136,negated_conjecture,
not(and(b,t1)) = t3,
t3 ).
cnf(c_0_137,negated_conjecture,
and(t1,not(and(b,t2))) = not(and(b,t2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_129]),c_0_60]) ).
cnf(c_0_138,negated_conjecture,
and(b,t2) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_129,c_0_130]),c_0_131]),c_0_48]) ).
cnf(c_0_139,plain,
and(X1,and(not(X1),X2)) = ll0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_56]),c_0_91]) ).
cnf(c_0_140,negated_conjecture,
and(t4,sum) = and(t5,t4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_134]),c_0_59]) ).
cnf(c_0_141,negated_conjecture,
not(t4) = and(t2,t3),
inference(spm,[status(thm)],[c_0_43,c_0_135]) ).
cnf(c_0_142,plain,
or(X1,and(X2,and(X1,X3))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_67]),c_0_55]),c_0_54]) ).
cnf(c_0_143,negated_conjecture,
and(t3,not(b)) = not(b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_136]),c_0_37]) ).
cnf(c_0_144,negated_conjecture,
and(t1,not(b)) = not(b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_138]),c_0_138]) ).
cnf(c_0_145,negated_conjecture,
not(t3) = and(b,t1),
inference(spm,[status(thm)],[c_0_43,c_0_136]) ).
cnf(c_0_146,plain,
and(X1,not(and(not(X2),X1))) = and(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_56]),c_0_49]),c_0_112]) ).
cnf(c_0_147,plain,
and(X1,and(X2,not(X1))) = ll0,
inference(spm,[status(thm)],[c_0_139,c_0_37]) ).
cnf(c_0_148,plain,
or(X1,and(X2,and(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_67,c_0_54]) ).
cnf(c_0_149,negated_conjecture,
and(t2,and(t3,t6)) = and(t2,t3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_140]),c_0_141]),c_0_50]),c_0_54]),c_0_141]) ).
cnf(c_0_150,negated_conjecture,
or(t3,and(X1,not(b))) = t3,
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_151,negated_conjecture,
xor(b,t1) = 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_45,c_0_144]),c_0_74]),c_0_54]),c_0_61]),c_0_76]),c_0_60]),c_0_136]),c_0_58]) ).
cnf(c_0_152,negated_conjecture,
xor(b,t3) = not(and(b,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_45,c_0_143]),c_0_145]),c_0_54]),c_0_37]),c_0_75]),c_0_76]),c_0_136]),c_0_58]) ).
cnf(c_0_153,plain,
xor(X1,or(X2,X1)) = and(not(X1),X2),
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_45,c_0_146]),c_0_104]),c_0_41]),c_0_147]),c_0_91]),c_0_104]) ).
cnf(c_0_154,negated_conjecture,
or(t6,and(t2,t3)) = t6,
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_155,negated_conjecture,
or(t6,and(cin,t4)) = t6,
inference(spm,[status(thm)],[c_0_67,c_0_115]) ).
cnf(c_0_156,plain,
or(X1,or(X2,and(not(X1),not(X2)))) = ll1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_41]),c_0_117]) ).
cnf(c_0_157,negated_conjecture,
or(t3,and(not(b),X1)) = t3,
inference(spm,[status(thm)],[c_0_150,c_0_37]) ).
cnf(c_0_158,negated_conjecture,
not(and(b,t3)) = t1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_151]),c_0_152]) ).
cnf(c_0_159,negated_conjecture,
not(xor(t3,and(b,t3))) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_152]),c_0_110]) ).
cnf(c_0_160,negated_conjecture,
xor(t6,and(t2,t3)) = and(cin,t4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_135]),c_0_115]),c_0_58]) ).
cnf(c_0_161,negated_conjecture,
xor(t6,and(cin,t4)) = and(t5,t6),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_155]),c_0_44]),c_0_58]) ).
cnf(c_0_162,negated_conjecture,
or(b,t3) = ll1,
inference(spm,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_163,negated_conjecture,
and(b,t3) = and(a,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_158]),c_0_74]) ).
cnf(c_0_164,negated_conjecture,
xor(t3,and(b,t3)) = not(b),
inference(spm,[status(thm)],[c_0_43,c_0_159]) ).
cnf(c_0_165,negated_conjecture,
and(t2,t3) = and(t5,t6),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_160]),c_0_161]) ).
cnf(c_0_166,negated_conjecture,
or(b,and(X1,t3)) = or(b,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_162]),c_0_48]) ).
cnf(c_0_167,negated_conjecture,
or(b,t2) = t2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_138]),c_0_39]) ).
cnf(c_0_168,negated_conjecture,
or(t3,and(a,b)) = t3,
inference(spm,[status(thm)],[c_0_67,c_0_163]) ).
cnf(c_0_169,negated_conjecture,
xor(t3,and(a,b)) = not(b),
inference(rw,[status(thm)],[c_0_164,c_0_163]) ).
cnf(c_0_170,negated_conjecture,
or(t3,and(t5,t6)) = t3,
inference(spm,[status(thm)],[c_0_67,c_0_165]) ).
cnf(c_0_171,negated_conjecture,
not(and(t5,t6)) = t4,
inference(rw,[status(thm)],[c_0_135,c_0_165]) ).
cnf(c_0_172,negated_conjecture,
or(b,and(t5,t6)) = t2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_165]),c_0_167]) ).
cnf(c_0_173,negated_conjecture,
not(b) = and(t1,t3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_168]),c_0_60]),c_0_58]),c_0_169]) ).
cnf(c_0_174,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_52,c_0_135]),c_0_78]),c_0_54]),c_0_78]) ).
cnf(c_0_175,negated_conjecture,
and(b,and(t1,t4)) = and(b,t1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_170]),c_0_145]),c_0_145]),c_0_171]),c_0_54]) ).
cnf(c_0_176,negated_conjecture,
and(t1,and(t4,t3)) = and(a,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_41,c_0_172]),c_0_78]),c_0_173]),c_0_171]),c_0_54]),c_0_37]) ).
cnf(c_0_177,negated_conjecture,
or(and(a,t1),and(t1,t4)) = and(t1,t4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_174]),c_0_39]) ).
cnf(c_0_178,negated_conjecture,
or(t4,and(b,t1)) = t4,
inference(spm,[status(thm)],[c_0_148,c_0_175]) ).
cnf(c_0_179,negated_conjecture,
or(t3,and(a,t1)) = t3,
inference(spm,[status(thm)],[c_0_148,c_0_176]) ).
cnf(c_0_180,negated_conjecture,
or(t2,and(t5,t6)) = t2,
inference(spm,[status(thm)],[c_0_42,c_0_165]) ).
cnf(c_0_181,negated_conjecture,
and(t2,not(and(t1,t4))) = not(and(t1,t4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_177]),c_0_63]) ).
cnf(c_0_182,negated_conjecture,
xor(t4,and(b,t1)) = and(t4,t3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_178]),c_0_136]),c_0_37]),c_0_58]) ).
cnf(c_0_183,negated_conjecture,
xor(t3,and(a,t1)) = and(t5,t6),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_179]),c_0_63]),c_0_165]),c_0_58]) ).
cnf(c_0_184,negated_conjecture,
xor(t3,and(t5,t6)) = and(t4,t3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_170]),c_0_171]),c_0_58]) ).
cnf(c_0_185,negated_conjecture,
or(t4,and(a,t1)) = t4,
inference(spm,[status(thm)],[c_0_148,c_0_174]) ).
cnf(c_0_186,negated_conjecture,
xor(t2,and(t5,t6)) = and(t4,t2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_180]),c_0_171]),c_0_58]) ).
cnf(c_0_187,negated_conjecture,
xor(t2,and(t1,t4)) = not(and(t1,and(t4,t2))),
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_45,c_0_181]),c_0_78]),c_0_54]),c_0_75]),c_0_174]),c_0_76]),c_0_63]),c_0_54]) ).
cnf(c_0_188,negated_conjecture,
xor(t4,and(t4,t3)) = and(b,t1),
inference(spm,[status(thm)],[c_0_86,c_0_182]) ).
cnf(c_0_189,negated_conjecture,
and(t4,t3) = and(a,t1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_183]),c_0_184]) ).
cnf(c_0_190,negated_conjecture,
xor(t4,and(a,t1)) = and(t4,t2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_185]),c_0_63]),c_0_58]),c_0_37]) ).
cnf(c_0_191,negated_conjecture,
and(t4,t2) = and(b,t4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_172]),c_0_58]),c_0_186]),c_0_171]),c_0_37]) ).
cnf(c_0_192,negated_conjecture,
xor(t2,and(t4,t2)) = and(t5,t6),
inference(spm,[status(thm)],[c_0_86,c_0_186]) ).
cnf(c_0_193,negated_conjecture,
not(xor(t2,and(t1,and(t4,t2)))) = and(t1,t4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_187]),c_0_110]) ).
cnf(c_0_194,negated_conjecture,
and(b,t4) = and(b,t1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_188,c_0_189]),c_0_190]),c_0_191]) ).
cnf(c_0_195,negated_conjecture,
xor(t2,and(b,t4)) = and(t5,t6),
inference(rw,[status(thm)],[c_0_192,c_0_191]) ).
cnf(c_0_196,negated_conjecture,
or(t4,and(t2,t3)) = ll1,
inference(spm,[status(thm)],[c_0_92,c_0_141]) ).
cnf(c_0_197,negated_conjecture,
xor(t2,and(t1,and(t4,t2))) = not(and(t1,t4)),
inference(spm,[status(thm)],[c_0_43,c_0_193]) ).
cnf(c_0_198,negated_conjecture,
and(t4,t2) = and(b,t1),
inference(rw,[status(thm)],[c_0_191,c_0_194]) ).
cnf(c_0_199,negated_conjecture,
xor(t2,and(b,t1)) = and(t5,t6),
inference(rw,[status(thm)],[c_0_195,c_0_194]) ).
cnf(c_0_200,negated_conjecture,
or(t4,and(t5,t6)) = ll1,
inference(rw,[status(thm)],[c_0_196,c_0_165]) ).
cnf(c_0_201,negated_conjecture,
not(and(t1,t4)) = and(t5,t6),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_198]),c_0_84]),c_0_37]),c_0_199]) ).
cnf(c_0_202,plain,
or(X1,or(X2,X3)) = or(X2,or(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_39]),c_0_117]) ).
cnf(c_0_203,negated_conjecture,
or(t5,t4) = ll1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_200]),c_0_125]),c_0_125]),c_0_39]) ).
cnf(c_0_204,negated_conjecture,
and(t1,t4) = t4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_201]),c_0_171]) ).
cnf(c_0_205,negated_conjecture,
or(t5,or(X1,t4)) = ll1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_203]),c_0_125]) ).
cnf(c_0_206,negated_conjecture,
or(t1,t4) = t1,
inference(spm,[status(thm)],[c_0_42,c_0_204]) ).
cnf(c_0_207,plain,
xor(X1,or(X1,X2)) = and(not(X1),X2),
inference(spm,[status(thm)],[c_0_153,c_0_39]) ).
cnf(c_0_208,negated_conjecture,
or(t1,t5) = ll1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_206]),c_0_39]) ).
cnf(c_0_209,negated_conjecture,
and(a,and(b,t5)) = 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_207,c_0_208]),c_0_100]),c_0_74]),c_0_74]),c_0_54]) ).
cnf(c_0_210,negated_conjecture,
not(and(t1,t5)) = carry,
carry ).
cnf(c_0_211,negated_conjecture,
or(t6,and(t5,t4)) = ll1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_50]),c_0_39]) ).
cnf(c_0_212,negated_conjecture,
or(t5,and(a,b)) = t5,
inference(spm,[status(thm)],[c_0_148,c_0_209]) ).
cnf(c_0_213,negated_conjecture,
or(and(carry,X1),and(t1,and(t5,not(X1)))) = xor(and(t1,t5),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_210]),c_0_54]),c_0_39]) ).
cnf(c_0_214,negated_conjecture,
and(cin,and(t5,t4)) = ll0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_44]),c_0_54]),c_0_37]) ).
cnf(c_0_215,plain,
and(or(X1,X2),or(X2,X3)) = or(X2,and(X1,X3)),
inference(spm,[status(thm)],[c_0_101,c_0_39]) ).
cnf(c_0_216,negated_conjecture,
or(t5,t6) = ll1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_211]),c_0_125]),c_0_125]),c_0_39]) ).
cnf(c_0_217,negated_conjecture,
xor(t5,and(a,b)) = and(t1,t5),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_212]),c_0_60]),c_0_58]) ).
cnf(c_0_218,negated_conjecture,
xor(t5,and(t1,t5)) = and(t5,carry),
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_213,c_0_53]),c_0_37]),c_0_114]),c_0_37]),c_0_214]),c_0_46]),c_0_49]),c_0_58]) ).
cnf(c_0_219,negated_conjecture,
or(t6,and(t5,X1)) = or(t6,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_216]),c_0_103]) ).
cnf(c_0_220,negated_conjecture,
and(t5,carry) = and(a,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_217]),c_0_218]) ).
cnf(c_0_221,negated_conjecture,
or(t1,and(a,b)) = ll1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_60]),c_0_39]) ).
cnf(c_0_222,negated_conjecture,
or(t6,and(a,b)) = or(carry,t6),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_220]),c_0_39]) ).
cnf(c_0_223,negated_conjecture,
not(carry) = and(t1,t5),
inference(spm,[status(thm)],[c_0_43,c_0_210]) ).
cnf(c_0_224,negated_conjecture,
or(a,t1) = ll1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_221]),c_0_125]),c_0_125]),c_0_39]) ).
cnf(c_0_225,negated_conjecture,
and(t1,and(t5,t4)) = 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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_222]),c_0_41]),c_0_223]),c_0_65]),c_0_54]),c_0_75]),c_0_65]),c_0_60]),c_0_54]),c_0_37]),c_0_204]) ).
cnf(c_0_226,negated_conjecture,
or(a,and(X1,t2)) = or(a,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_131]),c_0_48]) ).
cnf(c_0_227,negated_conjecture,
or(a,and(X1,t1)) = or(a,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_224]),c_0_48]) ).
cnf(c_0_228,plain,
xor(ll1,X1) = not(X1),
inference(spm,[status(thm)],[c_0_58,c_0_100]) ).
cnf(c_0_229,negated_conjecture,
and(a,and(b,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_52,c_0_225]),c_0_74]),c_0_50]),c_0_54]),c_0_74]) ).
cnf(c_0_230,negated_conjecture,
or(carry,and(t1,t5)) = ll1,
inference(spm,[status(thm)],[c_0_92,c_0_223]) ).
cnf(c_0_231,negated_conjecture,
and(t1,or(a,t4)) = and(t1,t4),
inference(rw,[status(thm)],[c_0_177,c_0_130]) ).
cnf(c_0_232,negated_conjecture,
or(a,t4) = or(a,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_226,c_0_198]),c_0_227]) ).
cnf(c_0_233,negated_conjecture,
or(t3,and(b,t1)) = ll1,
inference(spm,[status(thm)],[c_0_92,c_0_145]) ).
cnf(c_0_234,negated_conjecture,
and(a,and(t1,t3)) = and(a,t1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_179]),c_0_54]) ).
cnf(c_0_235,plain,
or(and(X1,X2),and(X3,X1)) = and(X1,or(X2,X3)),
inference(spm,[status(thm)],[c_0_122,c_0_37]) ).
cnf(c_0_236,plain,
xor(X1,xor(X2,X3)) = xor(X2,xor(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_58]),c_0_70]) ).
cnf(c_0_237,plain,
xor(not(X1),X2) = not(xor(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_228]),c_0_228]) ).
cnf(c_0_238,negated_conjecture,
or(carry,t6) = t6,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_229]),c_0_222]) ).
cnf(c_0_239,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_101,c_0_230]),c_0_54]),c_0_103]) ).
cnf(c_0_240,negated_conjecture,
or(t1,carry) = ll1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_230]),c_0_125]),c_0_125]),c_0_39]) ).
cnf(c_0_241,negated_conjecture,
and(t1,or(a,b)) = and(t1,t4),
inference(rw,[status(thm)],[c_0_231,c_0_232]) ).
cnf(c_0_242,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_101,c_0_233]),c_0_54]),c_0_103]) ).
cnf(c_0_243,negated_conjecture,
and(t1,or(a,t3)) = and(t1,t3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_234]),c_0_235]),c_0_39]) ).
cnf(c_0_244,negated_conjecture,
and(b,and(t1,t3)) = ll0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_136]),c_0_54]) ).
cnf(c_0_245,plain,
or(X1,or(X2,X1)) = or(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_55]),c_0_117]) ).
cnf(c_0_246,negated_conjecture,
xor(a,xor(X1,t1)) = xor(X1,t2),
inference(spm,[status(thm)],[c_0_236,c_0_87]) ).
cnf(c_0_247,plain,
or(and(X1,X2),and(not(X1),not(X2))) = not(xor(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_43]),c_0_39]),c_0_237]) ).
cnf(c_0_248,negated_conjecture,
and(carry,t6) = carry,
inference(spm,[status(thm)],[c_0_55,c_0_238]) ).
cnf(c_0_249,negated_conjecture,
or(carry,and(t5,X1)) = or(carry,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_75]),c_0_239]) ).
cnf(c_0_250,negated_conjecture,
or(carry,and(t1,X1)) = or(carry,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_240]),c_0_103]) ).
cnf(c_0_251,negated_conjecture,
and(t1,or(a,b)) = t4,
inference(rw,[status(thm)],[c_0_241,c_0_204]) ).
cnf(c_0_252,plain,
or(X1,or(X2,X3)) = or(X3,or(X1,X2)),
inference(spm,[status(thm)],[c_0_39,c_0_117]) ).
cnf(c_0_253,negated_conjecture,
or(a,t3) = t3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_242,c_0_243]),c_0_244]),c_0_49]),c_0_245]),c_0_39]) ).
cnf(c_0_254,negated_conjecture,
xor(b,t2) = xor(a,t3),
inference(spm,[status(thm)],[c_0_246,c_0_151]) ).
cnf(c_0_255,negated_conjecture,
not(xor(carry,t6)) = or(t4,carry),
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_247,c_0_248]),c_0_223]),c_0_65]),c_0_54]),c_0_75]),c_0_225]),c_0_249]),c_0_39]) ).
cnf(c_0_256,negated_conjecture,
xor(carry,t6) = and(t1,and(t5,t6)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_238]),c_0_223]),c_0_54]) ).
cnf(c_0_257,negated_conjecture,
or(t7,and(cin,t4)) = t7,
inference(spm,[status(thm)],[c_0_67,c_0_113]) ).
cnf(c_0_258,plain,
or(X1,or(X1,X2)) = or(X1,X2),
inference(spm,[status(thm)],[c_0_117,c_0_57]) ).
cnf(c_0_259,negated_conjecture,
or(a,or(b,carry)) = or(t4,carry),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_250,c_0_251]),c_0_39]),c_0_252]),c_0_39]),c_0_202]) ).
cnf(c_0_260,negated_conjecture,
and(a,t3) = a,
inference(spm,[status(thm)],[c_0_55,c_0_253]) ).
cnf(c_0_261,negated_conjecture,
or(b,and(a,t1)) = or(b,t4),
inference(spm,[status(thm)],[c_0_166,c_0_189]) ).
cnf(c_0_262,negated_conjecture,
xor(a,t3) = and(t2,not(b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_167]),c_0_254]),c_0_37]) ).
cnf(c_0_263,plain,
and(X1,and(X2,X3)) = and(X2,and(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_37]),c_0_54]) ).
cnf(c_0_264,negated_conjecture,
not(and(t1,and(t5,t6))) = or(t4,carry),
inference(rw,[status(thm)],[c_0_255,c_0_256]) ).
cnf(c_0_265,negated_conjecture,
and(t4,or(a,b)) = t4,
inference(spm,[status(thm)],[c_0_69,c_0_232]) ).
cnf(c_0_266,negated_conjecture,
and(cin,and(t4,t7)) = and(cin,t4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_257]),c_0_54]) ).
cnf(c_0_267,negated_conjecture,
or(and(cin,or(a,b)),and(not(cin),and(a,b))) = carry_def,
carry_def ).
cnf(c_0_268,negated_conjecture,
or(a,or(t4,carry)) = or(t4,carry),
inference(spm,[status(thm)],[c_0_258,c_0_259]) ).
cnf(c_0_269,negated_conjecture,
or(t4,carry) = or(b,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(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_247,c_0_138]),c_0_173]),c_0_78]),c_0_54]),c_0_114]),c_0_37]),c_0_260]),c_0_37]),c_0_84]),c_0_37]),c_0_261]),c_0_254]),c_0_262]),c_0_173]),c_0_263]),c_0_165]),c_0_264]) ).
cnf(c_0_270,negated_conjecture,
or(a,or(b,t4)) = or(a,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_265]),c_0_117]) ).
cnf(c_0_271,negated_conjecture,
or(and(cin,t4),and(t4,t7)) = and(t4,t7),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_266]),c_0_39]) ).
cnf(c_0_272,negated_conjecture,
or(t7,and(X1,not(cin))) = t7,
inference(spm,[status(thm)],[c_0_142,c_0_81]) ).
cnf(c_0_273,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_267,c_0_37]),c_0_54]),c_0_39]) ).
cnf(c_0_274,negated_conjecture,
and(cin,or(X1,and(t5,t4))) = and(cin,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_214]),c_0_49]) ).
cnf(c_0_275,negated_conjecture,
or(b,t4) = or(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_268,c_0_269]),c_0_270]),c_0_269]) ).
cnf(c_0_276,negated_conjecture,
and(t5,not(and(t4,t7))) = not(and(t4,t7)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_271]),c_0_44]) ).
cnf(c_0_277,negated_conjecture,
or(t7,and(not(cin),X1)) = t7,
inference(spm,[status(thm)],[c_0_272,c_0_37]) ).
cnf(c_0_278,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_245,c_0_273]),c_0_39]),c_0_273]),c_0_39]) ).
cnf(c_0_279,negated_conjecture,
and(cin,or(a,b)) = and(cin,carry),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_274,c_0_249]),c_0_39]),c_0_269]),c_0_275]) ).
cnf(c_0_280,negated_conjecture,
xor(a,xor(t1,X1)) = xor(t2,X1),
inference(spm,[status(thm)],[c_0_70,c_0_87]) ).
cnf(c_0_281,negated_conjecture,
xor(t1,t3) = b,
inference(spm,[status(thm)],[c_0_108,c_0_151]) ).
cnf(c_0_282,negated_conjecture,
xor(t5,and(t4,t7)) = not(and(t4,and(t5,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_45,c_0_276]),c_0_53]),c_0_54]),c_0_75]),c_0_266]),c_0_76]),c_0_44]),c_0_54]),c_0_37]) ).
cnf(c_0_283,negated_conjecture,
or(cin,t7) = ll1,
inference(spm,[status(thm)],[c_0_156,c_0_277]) ).
cnf(c_0_284,negated_conjecture,
or(carry_def,and(cin,carry)) = carry_def,
inference(rw,[status(thm)],[c_0_278,c_0_279]) ).
cnf(c_0_285,negated_conjecture,
xor(t2,t3) = xor(a,b),
inference(spm,[status(thm)],[c_0_280,c_0_281]) ).
cnf(c_0_286,negated_conjecture,
xor(t5,and(t4,t7)) = not(and(t5,and(t4,t7))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_282,c_0_114]),c_0_37]) ).
cnf(c_0_287,negated_conjecture,
and(t4,t7) = t4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_271,c_0_130]),c_0_283]),c_0_48]) ).
cnf(c_0_288,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_41,c_0_273]) ).
cnf(c_0_289,negated_conjecture,
and(cin,and(carry,carry_def)) = and(cin,carry),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_284]),c_0_54]) ).
cnf(c_0_290,negated_conjecture,
or(and(a,and(b,X1)),and(t1,not(X1))) = xor(t1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_74]),c_0_54]),c_0_39]) ).
cnf(c_0_291,negated_conjecture,
not(t4) = and(t5,t6),
inference(rw,[status(thm)],[c_0_141,c_0_165]) ).
cnf(c_0_292,negated_conjecture,
and(a,and(b,t1)) = ll0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_60]),c_0_54]) ).
cnf(c_0_293,negated_conjecture,
xor(a,and(t2,not(b))) = t3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_285]),c_0_236]),c_0_58]),c_0_254]),c_0_262]) ).
cnf(c_0_294,negated_conjecture,
xor(cin,xor(t5,X1)) = xor(t7,X1),
inference(spm,[status(thm)],[c_0_70,c_0_94]) ).
cnf(c_0_295,negated_conjecture,
xor(t5,t4) = t6,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_286,c_0_287]),c_0_287]),c_0_50]) ).
cnf(c_0_296,negated_conjecture,
and(not(carry_def),not(and(a,and(b,not(cin))))) = not(carry_def),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_288]),c_0_37]) ).
cnf(c_0_297,negated_conjecture,
not(and(a,and(b,not(X1)))) = or(X1,t1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_74]),c_0_37]),c_0_54]) ).
cnf(c_0_298,negated_conjecture,
or(t1,and(carry,X1)) = or(t1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_240]),c_0_103]) ).
cnf(c_0_299,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_67,c_0_289]),c_0_235]),c_0_39]) ).
cnf(c_0_300,negated_conjecture,
xor(xor(a,b),cin) = sum_def,
sum_def ).
cnf(c_0_301,negated_conjecture,
xor(t1,t4) = and(t1,and(t5,t6)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_290,c_0_291]),c_0_194]),c_0_292]),c_0_91]) ).
cnf(c_0_302,negated_conjecture,
xor(a,and(t1,and(t5,t6))) = t3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_293,c_0_173]),c_0_263]),c_0_165]) ).
cnf(c_0_303,negated_conjecture,
or(t4,t7) = t7,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_287]),c_0_39]) ).
cnf(c_0_304,negated_conjecture,
xor(t4,t7) = xor(cin,t6),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_294,c_0_295]),c_0_58]) ).
cnf(c_0_305,negated_conjecture,
or(t5,sum) = t5,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_258,c_0_120]),c_0_39]) ).
cnf(c_0_306,plain,
and(not(X1),and(X2,X1)) = ll0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_139]),c_0_46]),c_0_54]) ).
cnf(c_0_307,plain,
xor(X1,and(not(X1),X2)) = or(X2,X1),
inference(spm,[status(thm)],[c_0_86,c_0_153]) ).
cnf(c_0_308,negated_conjecture,
and(not(carry_def),or(cin,t1)) = not(carry_def),
inference(rw,[status(thm)],[c_0_296,c_0_297]) ).
cnf(c_0_309,negated_conjecture,
or(cin,or(t1,carry_def)) = or(t1,carry_def),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_298,c_0_299]),c_0_298]),c_0_202]) ).
cnf(c_0_310,negated_conjecture,
or(carry,and(cin,t4)) = carry,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_56]),c_0_46]),c_0_49]),c_0_53]) ).
cnf(c_0_311,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_52,c_0_210]),c_0_74]),c_0_54]),c_0_74]) ).
cnf(c_0_312,negated_conjecture,
xor(cin,xor(a,b)) = sum_def,
inference(rw,[status(thm)],[c_0_300,c_0_58]) ).
cnf(c_0_313,negated_conjecture,
xor(t4,t2) = t3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_280,c_0_301]),c_0_302]),c_0_58]) ).
cnf(c_0_314,negated_conjecture,
xor(t5,t7) = cin,
inference(spm,[status(thm)],[c_0_108,c_0_94]) ).
cnf(c_0_315,negated_conjecture,
xor(cin,t6) = and(t5,and(t6,t7)),
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_303]),c_0_141]),c_0_165]),c_0_54]),c_0_304]) ).
cnf(c_0_316,negated_conjecture,
xor(t5,sum) = 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(spm,[status(thm)],[c_0_153,c_0_305]),c_0_93]),c_0_54]),c_0_37]),c_0_58]),c_0_263]) ).
cnf(c_0_317,plain,
xor(X1,and(not(X2),X1)) = and(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_146]),c_0_306]),c_0_49]) ).
cnf(c_0_318,plain,
and(X1,and(X2,or(X3,and(X1,X2)))) = and(X1,X2),
inference(spm,[status(thm)],[c_0_54,c_0_69]) ).
cnf(c_0_319,plain,
and(X1,or(X2,and(X3,X1))) = and(X1,or(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_84]),c_0_122]) ).
cnf(c_0_320,negated_conjecture,
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(spm,[status(thm)],[c_0_307,c_0_308]),c_0_110]),c_0_71]),c_0_47]),c_0_117]),c_0_309]) ).
cnf(c_0_321,negated_conjecture,
xor(carry,and(cin,t4)) = and(t5,carry),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_310]),c_0_44]),c_0_58]) ).
cnf(c_0_322,negated_conjecture,
or(carry,and(a,b)) = carry,
inference(spm,[status(thm)],[c_0_148,c_0_311]) ).
cnf(c_0_323,negated_conjecture,
xor(cin,sum_def) = xor(a,b),
inference(spm,[status(thm)],[c_0_86,c_0_312]) ).
cnf(c_0_324,negated_conjecture,
xor(a,b) = t4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_313]),c_0_285]) ).
cnf(c_0_325,negated_conjecture,
xor(t5,xor(X1,t7)) = xor(X1,cin),
inference(spm,[status(thm)],[c_0_236,c_0_314]) ).
cnf(c_0_326,negated_conjecture,
xor(t4,t7) = and(t5,and(t6,t7)),
inference(rw,[status(thm)],[c_0_304,c_0_315]) ).
cnf(c_0_327,negated_conjecture,
xor(t5,and(t5,and(t6,t7))) = sum,
inference(spm,[status(thm)],[c_0_86,c_0_316]) ).
cnf(c_0_328,plain,
not(xor(X1,and(X1,X2))) = not(and(X1,not(and(X1,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_52]),c_0_43]),c_0_237]),c_0_75]),c_0_76]) ).
cnf(c_0_329,plain,
xor(X1,and(X1,X2)) = and(not(X2),X1),
inference(spm,[status(thm)],[c_0_86,c_0_317]) ).
cnf(c_0_330,plain,
and(X1,and(X2,or(X3,X1))) = and(X1,X2),
inference(rw,[status(thm)],[c_0_318,c_0_319]) ).
cnf(c_0_331,negated_conjecture,
and(not(and(cin,carry)),or(cin,t1)) = not(carry_def),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_288,c_0_297]),c_0_279]),c_0_37]) ).
cnf(c_0_332,negated_conjecture,
and(t1,not(carry_def)) = not(carry_def),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_320]),c_0_100]),c_0_37]) ).
cnf(c_0_333,negated_conjecture,
xor(carry,and(t5,carry)) = and(cin,t4),
inference(spm,[status(thm)],[c_0_86,c_0_321]) ).
cnf(c_0_334,negated_conjecture,
xor(carry,and(a,b)) = and(t1,carry),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_322]),c_0_60]),c_0_58]) ).
cnf(c_0_335,negated_conjecture,
xor(cin,sum_def) = t4,
inference(rw,[status(thm)],[c_0_323,c_0_324]) ).
cnf(c_0_336,negated_conjecture,
xor(cin,t4) = sum,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_325,c_0_326]),c_0_327]),c_0_58]) ).
cnf(c_0_337,plain,
not(and(X1,not(and(X1,X2)))) = not(and(not(X2),X1)),
inference(rw,[status(thm)],[c_0_328,c_0_329]) ).
cnf(c_0_338,negated_conjecture,
and(t1,not(and(cin,carry))) = not(carry_def),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_330,c_0_331]),c_0_332]) ).
cnf(c_0_339,negated_conjecture,
and(t1,carry) = and(cin,t4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_333,c_0_220]),c_0_334]) ).
cnf(c_0_340,negated_conjecture,
( sum != sum_def
| carry != carry_def ),
prove_circuit ).
cnf(c_0_341,negated_conjecture,
sum_def = sum,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_335]),c_0_336]) ).
cnf(c_0_342,negated_conjecture,
not(and(t1,carry_def)) = t5,
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_337,c_0_338]),c_0_43]),c_0_43]),c_0_54]),c_0_37]),c_0_339]),c_0_75]),c_0_44]) ).
cnf(c_0_343,negated_conjecture,
carry_def != carry,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_340,c_0_341])]) ).
cnf(c_0_344,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_337,c_0_342]),c_0_210]),c_0_37]),c_0_332]),c_0_43]),c_0_343]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : HWV003-2 : TPTP v8.1.2. Released v2.7.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n001.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 2400
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Oct 3 06:15:52 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.50 Running first-order theorem proving
% 0.21/0.50 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.eDfCtm864f/E---3.1_24150.p
% 8.46/1.60 # Version: 3.1pre001
% 8.46/1.60 # Preprocessing class: FSMSSMSMSSSNFFN.
% 8.46/1.60 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.46/1.60 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 8.46/1.60 # Starting new_bool_3 with 300s (1) cores
% 8.46/1.60 # Starting new_bool_1 with 300s (1) cores
% 8.46/1.60 # Starting sh5l with 300s (1) cores
% 8.46/1.60 # sh5l with pid 24231 completed with status 0
% 8.46/1.60 # Result found by sh5l
% 8.46/1.60 # Preprocessing class: FSMSSMSMSSSNFFN.
% 8.46/1.60 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.46/1.60 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 8.46/1.60 # Starting new_bool_3 with 300s (1) cores
% 8.46/1.60 # Starting new_bool_1 with 300s (1) cores
% 8.46/1.60 # Starting sh5l with 300s (1) cores
% 8.46/1.60 # SinE strategy is gf500_gu_R04_F100_L20000
% 8.46/1.60 # Search class: FUHPM-FFMM21-MFFFFFNN
% 8.46/1.60 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 8.46/1.60 # Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 8.46/1.60 # SAT001_MinMin_p005000_rr_RG with pid 24236 completed with status 0
% 8.46/1.60 # Result found by SAT001_MinMin_p005000_rr_RG
% 8.46/1.60 # Preprocessing class: FSMSSMSMSSSNFFN.
% 8.46/1.60 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.46/1.60 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 8.46/1.60 # Starting new_bool_3 with 300s (1) cores
% 8.46/1.60 # Starting new_bool_1 with 300s (1) cores
% 8.46/1.60 # Starting sh5l with 300s (1) cores
% 8.46/1.60 # SinE strategy is gf500_gu_R04_F100_L20000
% 8.46/1.60 # Search class: FUHPM-FFMM21-MFFFFFNN
% 8.46/1.60 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 8.46/1.60 # Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 8.46/1.60 # Preprocessing time : 0.001 s
% 8.46/1.60 # Presaturation interreduction done
% 8.46/1.60
% 8.46/1.60 # Proof found!
% 8.46/1.60 # SZS status Unsatisfiable
% 8.46/1.60 # SZS output start CNFRefutation
% See solution above
% 8.46/1.60 # Parsed axioms : 36
% 8.46/1.60 # Removed by relevancy pruning/SinE : 0
% 8.46/1.60 # Initial clauses : 36
% 8.46/1.60 # Removed in clause preprocessing : 0
% 8.46/1.60 # Initial clauses in saturation : 36
% 8.46/1.60 # Processed clauses : 5208
% 8.46/1.60 # ...of these trivial : 2165
% 8.46/1.60 # ...subsumed : 747
% 8.46/1.60 # ...remaining for further processing : 2296
% 8.46/1.60 # Other redundant clauses eliminated : 0
% 8.46/1.60 # Clauses deleted for lack of memory : 0
% 8.46/1.60 # Backward-subsumed : 0
% 8.46/1.60 # Backward-rewritten : 965
% 8.46/1.60 # Generated clauses : 122511
% 8.46/1.60 # ...of the previous two non-redundant : 88504
% 8.46/1.60 # ...aggressively subsumed : 0
% 8.46/1.60 # Contextual simplify-reflections : 0
% 8.46/1.60 # Paramodulations : 122511
% 8.46/1.60 # Factorizations : 0
% 8.46/1.60 # NegExts : 0
% 8.46/1.60 # Equation resolutions : 0
% 8.46/1.60 # Total rewrite steps : 265451
% 8.46/1.60 # Propositional unsat checks : 0
% 8.46/1.60 # Propositional check models : 0
% 8.46/1.60 # Propositional check unsatisfiable : 0
% 8.46/1.60 # Propositional clauses : 0
% 8.46/1.60 # Propositional clauses after purity: 0
% 8.46/1.60 # Propositional unsat core size : 0
% 8.46/1.60 # Propositional preprocessing time : 0.000
% 8.46/1.60 # Propositional encoding time : 0.000
% 8.46/1.60 # Propositional solver time : 0.000
% 8.46/1.60 # Success case prop preproc time : 0.000
% 8.46/1.60 # Success case prop encoding time : 0.000
% 8.46/1.60 # Success case prop solver time : 0.000
% 8.46/1.60 # Current number of processed clauses : 1295
% 8.46/1.60 # Positive orientable unit clauses : 1285
% 8.46/1.60 # Positive unorientable unit clauses: 9
% 8.46/1.60 # Negative unit clauses : 1
% 8.46/1.60 # Non-unit-clauses : 0
% 8.46/1.60 # Current number of unprocessed clauses: 82534
% 8.46/1.60 # ...number of literals in the above : 82534
% 8.46/1.60 # Current number of archived formulas : 0
% 8.46/1.60 # Current number of archived clauses : 1001
% 8.46/1.60 # Clause-clause subsumption calls (NU) : 0
% 8.46/1.60 # Rec. Clause-clause subsumption calls : 0
% 8.46/1.60 # Non-unit clause-clause subsumptions : 0
% 8.46/1.60 # Unit Clause-clause subsumption calls : 32
% 8.46/1.60 # Rewrite failures with RHS unbound : 0
% 8.46/1.60 # BW rewrite match attempts : 2546
% 8.46/1.60 # BW rewrite match successes : 896
% 8.46/1.60 # Condensation attempts : 0
% 8.46/1.60 # Condensation successes : 0
% 8.46/1.60 # Termbank termtop insertions : 1704626
% 8.46/1.60
% 8.46/1.60 # -------------------------------------------------
% 8.46/1.60 # User time : 0.975 s
% 8.46/1.60 # System time : 0.059 s
% 8.46/1.60 # Total time : 1.034 s
% 8.46/1.60 # Maximum resident set size: 1664 pages
% 8.46/1.60
% 8.46/1.60 # -------------------------------------------------
% 8.46/1.60 # User time : 0.975 s
% 8.46/1.60 # System time : 0.063 s
% 8.46/1.60 # Total time : 1.038 s
% 8.46/1.60 # Maximum resident set size: 1724 pages
% 8.46/1.60 % E---3.1 exiting
% 8.46/1.60 % E---3.1 exiting
%------------------------------------------------------------------------------