%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP779+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:41:14 PM UTC 2026
% Result : Theorem 78.79s 20.49s
% Output : CNFRefutation 78.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 16
% Syntax : Number of formulae : 285 ( 277 unt; 0 def)
% Number of atoms : 297 ( 269 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 24 ( 12 ~; 8 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 214 ( 0 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos05,axiom,
! [X3,X4,X1,X2] : product(product(X2,X1),product(X4,X3)) = product(product(X2,X4),product(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
fof(sos06,axiom,
! [X2] : product(X2,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
fof(sos08,axiom,
! [X5,X6,X7] :
( d(X5,X6,X7)
<=> product(X5,X6) = product(X6,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos08) ).
fof(sos02,axiom,
! [X1,X2] : product(X2,difference(X2,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
fof(sos01,axiom,
! [X1,X2] : difference(X2,product(X2,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
fof(sos13,axiom,
d(a,b1,c1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos13) ).
fof(sos15,axiom,
d(a1,b1,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos15) ).
fof(sos14,axiom,
d(a1,b,c1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos14) ).
fof(sos10,axiom,
d(b,bigA,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).
fof(sos07,axiom,
! [X1,X2] : product(product(product(X2,X1),X1),product(X1,product(X1,X2))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
fof(sos11,axiom,
d(bigB,a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).
fof(sos03,axiom,
! [X1,X2] : quotient(product(X2,X1),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
fof(sos04,axiom,
! [X1,X2] : product(quotient(X2,X1),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
fof(sos12,axiom,
d(b,a,bigC),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).
fof(goals,conjecture,
m(bigA,b1,bigC),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(sos09,axiom,
! [X8,X9,X10] :
( m(X8,X9,X10)
<=> product(product(X8,X9),product(X9,X10)) = product(X8,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
fof(c_0_16,plain,
! [X19,X20,X21,X22] : product(product(X22,X21),product(X20,X19)) = product(product(X22,X20),product(X21,X19)),
inference(variable_rename,[status(thm)],[sos05]) ).
fof(c_0_17,plain,
! [X23] : product(X23,X23) = X23,
inference(variable_rename,[status(thm)],[sos06]) ).
cnf(c_0_18,plain,
product(product(X1,X2),product(X3,X4)) = product(product(X1,X3),product(X2,X4)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,plain,
product(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_20,plain,
! [X26,X27,X28] :
( ( d(X26,X27,X28)
| product(X26,X27) != product(X27,X28) )
& ( product(X26,X27) = product(X27,X28)
| ~ d(X26,X27,X28) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos08])])]) ).
cnf(c_0_21,plain,
product(product(X1,X2),product(X3,X2)) = product(product(X1,X3),X2),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_22,plain,
! [X13,X14] : product(X14,difference(X14,X13)) = X13,
inference(variable_rename,[status(thm)],[sos02]) ).
fof(c_0_23,plain,
! [X11,X12] : difference(X12,product(X12,X11)) = X11,
inference(variable_rename,[status(thm)],[sos01]) ).
cnf(c_0_24,plain,
( ~ d(X1,X2,X3)
| product(X1,X2) = product(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
d(a,b1,c1),
inference(split_conjunct,[status(thm)],[sos13]) ).
cnf(c_0_26,plain,
product(product(X1,X2),X1) = product(X1,product(X2,X1)),
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_27,plain,
product(X1,difference(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
difference(X1,product(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
product(b1,c1) = product(a,b1),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
product(X1,product(difference(X1,X2),X1)) = product(X2,X1),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
d(a1,b1,c),
inference(split_conjunct,[status(thm)],[sos15]) ).
cnf(c_0_32,plain,
difference(b1,product(a,b1)) = c1,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
difference(X1,product(X2,X1)) = product(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_28,c_0_30]) ).
cnf(c_0_34,plain,
d(a1,b,c1),
inference(split_conjunct,[status(thm)],[sos14]) ).
cnf(c_0_35,plain,
product(a1,b1) = product(b1,c),
inference(spm,[status(thm)],[c_0_24,c_0_31]) ).
cnf(c_0_36,plain,
d(b,bigA,c),
inference(split_conjunct,[status(thm)],[sos10]) ).
fof(c_0_37,plain,
! [X24,X25] : product(product(product(X25,X24),X24),product(X24,product(X24,X25))) = X24,
inference(variable_rename,[status(thm)],[sos07]) ).
cnf(c_0_38,plain,
product(difference(b1,a),b1) = c1,
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,plain,
d(bigB,a,c),
inference(split_conjunct,[status(thm)],[sos11]) ).
cnf(c_0_40,plain,
product(a1,b) = product(b,c1),
inference(spm,[status(thm)],[c_0_24,c_0_34]) ).
cnf(c_0_41,plain,
product(difference(b1,a1),b1) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_35]),c_0_28]) ).
cnf(c_0_42,plain,
product(bigA,c) = product(b,bigA),
inference(spm,[status(thm)],[c_0_24,c_0_36]) ).
cnf(c_0_43,plain,
product(product(X1,X2),product(difference(X1,X3),X4)) = product(X3,product(X2,X4)),
inference(spm,[status(thm)],[c_0_18,c_0_27]) ).
fof(c_0_44,plain,
! [X15,X16] : quotient(product(X16,X15),X15) = X16,
inference(variable_rename,[status(thm)],[sos03]) ).
cnf(c_0_45,plain,
product(product(product(X1,X2),X2),product(X2,product(X2,X1))) = X2,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,plain,
product(difference(b1,difference(b1,a)),b1) = difference(b1,c1),
inference(spm,[status(thm)],[c_0_33,c_0_38]) ).
cnf(c_0_47,plain,
product(bigB,a) = product(a,c),
inference(spm,[status(thm)],[c_0_24,c_0_39]) ).
cnf(c_0_48,plain,
product(difference(b,a1),b) = c1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_40]),c_0_28]) ).
cnf(c_0_49,plain,
product(product(X1,a1),product(X2,b1)) = product(product(X1,X2),product(b1,c)),
inference(spm,[status(thm)],[c_0_18,c_0_35]) ).
cnf(c_0_50,plain,
product(product(a1,X1),product(b1,X2)) = product(product(b1,c),product(X1,X2)),
inference(spm,[status(thm)],[c_0_18,c_0_35]) ).
cnf(c_0_51,plain,
product(difference(b1,difference(b1,a1)),b1) = difference(b1,c),
inference(spm,[status(thm)],[c_0_33,c_0_41]) ).
cnf(c_0_52,plain,
difference(bigA,product(b,bigA)) = c,
inference(spm,[status(thm)],[c_0_28,c_0_42]) ).
cnf(c_0_53,plain,
product(product(b1,X1),c1) = product(a,product(X1,b1)),
inference(spm,[status(thm)],[c_0_43,c_0_38]) ).
cnf(c_0_54,plain,
quotient(product(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_55,plain,
product(product(difference(b1,c1),b1),a) = b1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_27]),c_0_27]) ).
cnf(c_0_56,plain,
product(difference(a,bigB),a) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_47]),c_0_28]) ).
cnf(c_0_57,plain,
product(product(X1,a1),product(X2,b)) = product(product(X1,X2),product(b,c1)),
inference(spm,[status(thm)],[c_0_18,c_0_40]) ).
cnf(c_0_58,plain,
product(product(a1,X1),product(b,X2)) = product(product(b,c1),product(X1,X2)),
inference(spm,[status(thm)],[c_0_18,c_0_40]) ).
cnf(c_0_59,plain,
product(difference(b,difference(b,a1)),b) = difference(b,c1),
inference(spm,[status(thm)],[c_0_33,c_0_48]) ).
cnf(c_0_60,plain,
product(product(b1,X1),c) = product(a1,product(X1,b1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_19]),c_0_21]) ).
cnf(c_0_61,plain,
product(product(difference(b1,c),b1),a1) = b1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_51]),c_0_27]),c_0_27]) ).
cnf(c_0_62,plain,
product(difference(bigA,b),bigA) = c,
inference(rw,[status(thm)],[c_0_52,c_0_33]) ).
cnf(c_0_63,plain,
difference(product(b1,X1),product(a,product(X1,b1))) = c1,
inference(spm,[status(thm)],[c_0_28,c_0_53]) ).
cnf(c_0_64,plain,
product(difference(b1,c1),b1) = quotient(b1,a),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_65,plain,
product(product(X1,bigB),product(X2,a)) = product(product(X1,X2),product(a,c)),
inference(spm,[status(thm)],[c_0_18,c_0_47]) ).
cnf(c_0_66,plain,
product(product(bigB,X1),product(a,X2)) = product(product(a,c),product(X1,X2)),
inference(spm,[status(thm)],[c_0_18,c_0_47]) ).
cnf(c_0_67,plain,
product(difference(a,difference(a,bigB)),a) = difference(a,c),
inference(spm,[status(thm)],[c_0_33,c_0_56]) ).
cnf(c_0_68,plain,
product(product(b,X1),c1) = product(a1,product(X1,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_19]),c_0_21]) ).
cnf(c_0_69,plain,
product(product(difference(b,c1),b),a1) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_59]),c_0_27]),c_0_27]) ).
cnf(c_0_70,plain,
difference(product(b1,X1),product(a1,product(X1,b1))) = c,
inference(spm,[status(thm)],[c_0_28,c_0_60]) ).
cnf(c_0_71,plain,
product(difference(b1,c),b1) = quotient(b1,a1),
inference(spm,[status(thm)],[c_0_54,c_0_61]) ).
cnf(c_0_72,plain,
product(difference(bigA,difference(bigA,b)),bigA) = difference(bigA,c),
inference(spm,[status(thm)],[c_0_33,c_0_62]) ).
cnf(c_0_73,plain,
quotient(product(X1,X2),product(difference(X2,X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_54,c_0_30]) ).
cnf(c_0_74,plain,
difference(c1,product(a,quotient(b1,a))) = c1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_27]) ).
cnf(c_0_75,plain,
product(product(a,X1),c) = product(bigB,product(X1,a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_19]),c_0_21]) ).
cnf(c_0_76,plain,
product(product(difference(a,c),a),bigB) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_67]),c_0_27]),c_0_27]) ).
cnf(c_0_77,plain,
difference(product(b,X1),product(a1,product(X1,b))) = c1,
inference(spm,[status(thm)],[c_0_28,c_0_68]) ).
cnf(c_0_78,plain,
product(difference(b,c1),b) = quotient(b,a1),
inference(spm,[status(thm)],[c_0_54,c_0_69]) ).
fof(c_0_79,plain,
! [X17,X18] : product(quotient(X18,X17),X17) = X18,
inference(variable_rename,[status(thm)],[sos04]) ).
cnf(c_0_80,plain,
difference(c,product(a1,quotient(b1,a1))) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_27]) ).
cnf(c_0_81,plain,
product(product(bigA,X1),c) = product(b,product(X1,bigA)),
inference(spm,[status(thm)],[c_0_43,c_0_62]) ).
cnf(c_0_82,plain,
product(product(difference(bigA,c),bigA),b) = bigA,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_72]),c_0_27]),c_0_27]) ).
cnf(c_0_83,plain,
d(b,a,bigC),
inference(split_conjunct,[status(thm)],[sos12]) ).
cnf(c_0_84,plain,
product(a,quotient(b1,a)) = c1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_19]),c_0_54]) ).
cnf(c_0_85,plain,
difference(product(a,X1),product(bigB,product(X1,a))) = c,
inference(spm,[status(thm)],[c_0_28,c_0_75]) ).
cnf(c_0_86,plain,
product(difference(a,c),a) = quotient(a,bigB),
inference(spm,[status(thm)],[c_0_54,c_0_76]) ).
cnf(c_0_87,plain,
difference(c1,product(a1,quotient(b,a1))) = c1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_27]) ).
cnf(c_0_88,plain,
product(quotient(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_89,plain,
product(a1,quotient(b1,a1)) = c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_80]),c_0_19]),c_0_54]) ).
cnf(c_0_90,plain,
difference(product(bigA,X1),product(b,product(X1,bigA))) = c,
inference(spm,[status(thm)],[c_0_28,c_0_81]) ).
cnf(c_0_91,plain,
product(difference(bigA,c),bigA) = quotient(bigA,b),
inference(spm,[status(thm)],[c_0_54,c_0_82]) ).
cnf(c_0_92,plain,
product(a,bigC) = product(b,a),
inference(spm,[status(thm)],[c_0_24,c_0_83]) ).
cnf(c_0_93,plain,
quotient(product(X1,product(X2,X1)),X1) = product(X1,X2),
inference(spm,[status(thm)],[c_0_54,c_0_26]) ).
cnf(c_0_94,plain,
quotient(b1,a) = difference(a,c1),
inference(spm,[status(thm)],[c_0_28,c_0_84]) ).
cnf(c_0_95,plain,
difference(c,product(bigB,quotient(a,bigB))) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_27]) ).
cnf(c_0_96,plain,
product(a1,quotient(b,a1)) = c1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_87]),c_0_19]),c_0_54]) ).
cnf(c_0_97,plain,
difference(a,product(a1,c1)) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_38]),c_0_27]) ).
cnf(c_0_98,plain,
product(product(X1,X2),product(X2,product(X2,quotient(X1,X2)))) = X2,
inference(spm,[status(thm)],[c_0_45,c_0_88]) ).
cnf(c_0_99,plain,
quotient(b1,a1) = difference(a1,c),
inference(spm,[status(thm)],[c_0_28,c_0_89]) ).
cnf(c_0_100,plain,
difference(c,product(b,quotient(bigA,b))) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_27]) ).
cnf(c_0_101,plain,
difference(product(X1,X2),product(X1,product(X2,X1))) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_26]) ).
cnf(c_0_102,plain,
difference(a,product(b,a)) = bigC,
inference(spm,[status(thm)],[c_0_28,c_0_92]) ).
cnf(c_0_103,plain,
quotient(product(X1,X2),X1) = product(X1,quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_93,c_0_88]) ).
cnf(c_0_104,plain,
product(difference(a,c1),a) = b1,
inference(spm,[status(thm)],[c_0_88,c_0_94]) ).
cnf(c_0_105,plain,
product(bigB,quotient(a,bigB)) = c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_95]),c_0_19]),c_0_54]) ).
cnf(c_0_106,plain,
product(product(product(b1,c),b1),product(b1,product(b1,a1))) = b1,
inference(spm,[status(thm)],[c_0_45,c_0_35]) ).
cnf(c_0_107,plain,
quotient(b,a1) = difference(a1,c1),
inference(spm,[status(thm)],[c_0_28,c_0_96]) ).
cnf(c_0_108,plain,
product(a1,c1) = product(a,c),
inference(spm,[status(thm)],[c_0_27,c_0_97]) ).
cnf(c_0_109,plain,
product(product(b1,a1),product(a1,c)) = a1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_27]) ).
cnf(c_0_110,plain,
product(b,quotient(bigA,b)) = c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_100]),c_0_19]),c_0_54]) ).
cnf(c_0_111,plain,
difference(product(X1,quotient(X2,X1)),product(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_101,c_0_88]) ).
cnf(c_0_112,plain,
product(difference(a,b),a) = bigC,
inference(rw,[status(thm)],[c_0_102,c_0_33]) ).
cnf(c_0_113,plain,
product(b1,quotient(c1,b1)) = a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_29]),c_0_54]) ).
cnf(c_0_114,plain,
quotient(product(b,c1),a1) = product(a1,quotient(b,a1)),
inference(spm,[status(thm)],[c_0_103,c_0_40]) ).
cnf(c_0_115,plain,
product(product(a,X1),b1) = product(c1,product(X1,a)),
inference(spm,[status(thm)],[c_0_43,c_0_104]) ).
cnf(c_0_116,plain,
quotient(a,bigB) = difference(bigB,c),
inference(spm,[status(thm)],[c_0_28,c_0_105]) ).
cnf(c_0_117,plain,
product(b1,product(product(c,b1),product(b1,a1))) = b1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_26]),c_0_18]),c_0_19]) ).
cnf(c_0_118,plain,
difference(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_19]) ).
cnf(c_0_119,plain,
product(product(b,a),product(a1,c)) = a1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_107]),c_0_27]),c_0_108]),c_0_18]) ).
cnf(c_0_120,plain,
quotient(a1,product(a1,c)) = product(b1,a1),
inference(spm,[status(thm)],[c_0_54,c_0_109]) ).
cnf(c_0_121,plain,
quotient(bigA,b) = difference(b,c),
inference(spm,[status(thm)],[c_0_28,c_0_110]) ).
cnf(c_0_122,plain,
difference(c,product(b,bigA)) = product(difference(c,bigA),c),
inference(spm,[status(thm)],[c_0_33,c_0_42]) ).
cnf(c_0_123,plain,
difference(product(a1,quotient(b,a1)),product(b,c1)) = a1,
inference(spm,[status(thm)],[c_0_111,c_0_40]) ).
cnf(c_0_124,plain,
product(difference(a,difference(a,b)),a) = difference(a,bigC),
inference(spm,[status(thm)],[c_0_33,c_0_112]) ).
cnf(c_0_125,plain,
difference(product(a1,quotient(b1,a1)),product(b1,c)) = a1,
inference(spm,[status(thm)],[c_0_111,c_0_35]) ).
cnf(c_0_126,plain,
quotient(c1,b1) = difference(b1,a),
inference(spm,[status(thm)],[c_0_28,c_0_113]) ).
cnf(c_0_127,plain,
quotient(product(b1,c),a1) = product(a1,quotient(b1,a1)),
inference(spm,[status(thm)],[c_0_103,c_0_35]) ).
cnf(c_0_128,plain,
product(difference(X1,quotient(X2,X1)),X1) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_33,c_0_88]) ).
cnf(c_0_129,plain,
quotient(product(b,c1),a1) = c1,
inference(rw,[status(thm)],[c_0_114,c_0_96]) ).
cnf(c_0_130,plain,
difference(a1,product(b,c1)) = b,
inference(spm,[status(thm)],[c_0_28,c_0_40]) ).
cnf(c_0_131,plain,
product(X1,quotient(difference(X1,X2),X1)) = quotient(X2,X1),
inference(spm,[status(thm)],[c_0_103,c_0_27]) ).
cnf(c_0_132,plain,
difference(product(a,X1),product(c1,product(X1,a))) = b1,
inference(spm,[status(thm)],[c_0_28,c_0_115]) ).
cnf(c_0_133,plain,
product(difference(a,c),a) = difference(bigB,c),
inference(rw,[status(thm)],[c_0_86,c_0_116]) ).
cnf(c_0_134,plain,
difference(c1,product(a,b1)) = product(difference(c1,b1),c1),
inference(spm,[status(thm)],[c_0_33,c_0_29]) ).
cnf(c_0_135,plain,
product(product(c,b1),product(b1,a1)) = b1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_117]),c_0_118]) ).
cnf(c_0_136,plain,
product(b1,a1) = product(b,a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_119]),c_0_120]) ).
cnf(c_0_137,plain,
product(difference(c,bigA),c) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_121]),c_0_27]),c_0_122]) ).
cnf(c_0_138,plain,
product(difference(c1,b),c1) = a1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_96]),c_0_33]) ).
cnf(c_0_139,plain,
product(product(a,X1),bigC) = product(b,product(X1,a)),
inference(spm,[status(thm)],[c_0_43,c_0_112]) ).
cnf(c_0_140,plain,
product(product(difference(a,bigC),a),b) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_124]),c_0_27]),c_0_27]) ).
cnf(c_0_141,plain,
difference(product(b1,quotient(X1,b1)),product(a1,X1)) = c,
inference(spm,[status(thm)],[c_0_70,c_0_88]) ).
cnf(c_0_142,plain,
product(difference(c,b1),c) = a1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_125,c_0_89]),c_0_33]) ).
cnf(c_0_143,plain,
product(product(c1,b1),product(b1,a)) = b1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_126]),c_0_27]) ).
cnf(c_0_144,plain,
quotient(product(b1,c),a1) = c,
inference(rw,[status(thm)],[c_0_127,c_0_89]) ).
cnf(c_0_145,plain,
difference(a1,product(b1,c)) = b1,
inference(spm,[status(thm)],[c_0_28,c_0_35]) ).
cnf(c_0_146,plain,
product(difference(a1,c1),a1) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_130]) ).
cnf(c_0_147,plain,
quotient(difference(X1,X2),X1) = difference(X1,quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_28,c_0_131]) ).
cnf(c_0_148,plain,
difference(c,product(c1,difference(bigB,c))) = b1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_27]) ).
cnf(c_0_149,plain,
product(difference(c1,b1),c1) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_94]),c_0_27]),c_0_134]) ).
cnf(c_0_150,plain,
product(product(c,b),product(b1,a)) = b1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_135,c_0_136]),c_0_18]) ).
cnf(c_0_151,plain,
product(c,b) = product(b,bigA),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_137]),c_0_42]) ).
cnf(c_0_152,plain,
product(product(c1,X1),a1) = product(b,product(X1,c1)),
inference(spm,[status(thm)],[c_0_43,c_0_138]) ).
cnf(c_0_153,plain,
difference(product(a,X1),product(b,product(X1,a))) = bigC,
inference(spm,[status(thm)],[c_0_28,c_0_139]) ).
cnf(c_0_154,plain,
product(difference(a,bigC),a) = quotient(a,b),
inference(spm,[status(thm)],[c_0_54,c_0_140]) ).
cnf(c_0_155,plain,
product(bigB,product(difference(a,X1),a)) = product(X1,c),
inference(spm,[status(thm)],[c_0_75,c_0_27]) ).
cnf(c_0_156,plain,
quotient(X1,difference(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_54,c_0_27]) ).
cnf(c_0_157,plain,
difference(product(b1,quotient(a1,b1)),a1) = c,
inference(spm,[status(thm)],[c_0_141,c_0_19]) ).
cnf(c_0_158,plain,
quotient(a1,c) = difference(c,b1),
inference(spm,[status(thm)],[c_0_54,c_0_142]) ).
cnf(c_0_159,plain,
quotient(b1,product(b1,a)) = product(c1,b1),
inference(spm,[status(thm)],[c_0_54,c_0_143]) ).
cnf(c_0_160,plain,
product(difference(a1,c),a1) = b1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_144]),c_0_145]) ).
cnf(c_0_161,plain,
product(b,product(a1,quotient(c1,a1))) = a1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_146]),c_0_147]),c_0_27]) ).
cnf(c_0_162,plain,
quotient(X1,product(X1,product(X1,X2))) = product(product(X2,X1),X1),
inference(spm,[status(thm)],[c_0_54,c_0_45]) ).
cnf(c_0_163,plain,
product(product(X1,a),product(X2,bigC)) = product(product(X1,X2),product(b,a)),
inference(spm,[status(thm)],[c_0_18,c_0_92]) ).
cnf(c_0_164,plain,
product(c1,difference(bigB,c)) = product(c,b1),
inference(spm,[status(thm)],[c_0_27,c_0_148]) ).
cnf(c_0_165,plain,
product(c1,a) = product(a,b1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_149]),c_0_29]) ).
cnf(c_0_166,plain,
product(product(b,b1),product(bigA,a)) = b1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_151]),c_0_18]) ).
cnf(c_0_167,plain,
product(a,quotient(a,bigB)) = product(c,a),
inference(spm,[status(thm)],[c_0_30,c_0_86]) ).
cnf(c_0_168,plain,
product(product(c1,X1),a) = product(b1,product(X1,c1)),
inference(spm,[status(thm)],[c_0_43,c_0_149]) ).
cnf(c_0_169,plain,
product(b,product(difference(bigA,X1),bigA)) = product(X1,c),
inference(spm,[status(thm)],[c_0_81,c_0_27]) ).
cnf(c_0_170,plain,
product(b,product(difference(c1,X1),c1)) = product(X1,a1),
inference(spm,[status(thm)],[c_0_152,c_0_27]) ).
cnf(c_0_171,plain,
difference(bigC,product(b,quotient(a,b))) = bigC,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_27]) ).
cnf(c_0_172,plain,
product(product(a1,X1),b) = product(c1,product(X1,a1)),
inference(spm,[status(thm)],[c_0_43,c_0_146]) ).
cnf(c_0_173,plain,
difference(bigB,product(X1,c)) = product(difference(a,X1),a),
inference(spm,[status(thm)],[c_0_28,c_0_155]) ).
cnf(c_0_174,plain,
product(b1,quotient(a1,b1)) = difference(c,b1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_158]) ).
cnf(c_0_175,plain,
product(c1,b1) = product(c,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_150]),c_0_159]) ).
cnf(c_0_176,plain,
product(product(a1,X1),b1) = product(c,product(X1,a1)),
inference(spm,[status(thm)],[c_0_43,c_0_160]) ).
cnf(c_0_177,plain,
product(a1,quotient(c1,a1)) = difference(b,a1),
inference(spm,[status(thm)],[c_0_28,c_0_161]) ).
cnf(c_0_178,plain,
product(product(difference(X1,X2),X1),X1) = quotient(X1,product(X1,X2)),
inference(spm,[status(thm)],[c_0_162,c_0_27]) ).
cnf(c_0_179,plain,
quotient(product(product(X1,X2),product(X3,X4)),product(X2,X4)) = product(X1,X3),
inference(spm,[status(thm)],[c_0_54,c_0_18]) ).
cnf(c_0_180,plain,
product(product(a,b1),product(difference(bigB,c),bigC)) = b1,
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_164]),c_0_165]),c_0_18]),c_0_151]),c_0_18]),c_0_166]) ).
cnf(c_0_181,plain,
product(a,difference(bigB,c)) = product(c,a),
inference(rw,[status(thm)],[c_0_167,c_0_116]) ).
cnf(c_0_182,plain,
product(b1,product(difference(c1,X1),c1)) = product(X1,a),
inference(spm,[status(thm)],[c_0_168,c_0_27]) ).
cnf(c_0_183,plain,
difference(b,product(X1,c)) = product(difference(bigA,X1),bigA),
inference(spm,[status(thm)],[c_0_28,c_0_169]) ).
cnf(c_0_184,plain,
product(b1,c) = product(c,a1),
inference(spm,[status(thm)],[c_0_88,c_0_144]) ).
cnf(c_0_185,plain,
difference(b,product(X1,a1)) = product(difference(c1,X1),c1),
inference(spm,[status(thm)],[c_0_28,c_0_170]) ).
cnf(c_0_186,plain,
product(b,quotient(a,b)) = bigC,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_171]),c_0_19]),c_0_54]) ).
cnf(c_0_187,plain,
quotient(product(a,c),bigB) = product(bigB,quotient(a,bigB)),
inference(spm,[status(thm)],[c_0_103,c_0_47]) ).
cnf(c_0_188,plain,
quotient(product(c1,product(X1,a1)),b) = product(a1,X1),
inference(spm,[status(thm)],[c_0_54,c_0_172]) ).
cnf(c_0_189,plain,
product(c1,product(difference(a,X1),a)) = product(X1,b1),
inference(spm,[status(thm)],[c_0_115,c_0_27]) ).
cnf(c_0_190,plain,
product(difference(a,difference(c,b1)),a) = difference(bigB,a1),
inference(spm,[status(thm)],[c_0_173,c_0_142]) ).
cnf(c_0_191,plain,
product(difference(c,b1),b1) = product(b1,a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_174]),c_0_88]) ).
cnf(c_0_192,plain,
difference(product(product(X1,X2),X2),X2) = product(X2,product(X2,X1)),
inference(spm,[status(thm)],[c_0_28,c_0_45]) ).
cnf(c_0_193,plain,
product(product(X1,b),product(a,bigA)) = product(product(X1,b1),c1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_29]),c_0_18]),c_0_175]),c_0_151]),c_0_18]) ).
cnf(c_0_194,plain,
product(difference(b,a1),b1) = product(c,c1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_177]),c_0_88]) ).
cnf(c_0_195,plain,
difference(X1,quotient(X1,product(X1,X2))) = quotient(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_178]),c_0_33]),c_0_178]),c_0_27]) ).
cnf(c_0_196,plain,
quotient(b1,product(b1,bigC)) = product(c,a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_180]),c_0_181]) ).
cnf(c_0_197,plain,
difference(b1,product(X1,a)) = product(difference(c1,X1),c1),
inference(spm,[status(thm)],[c_0_28,c_0_182]) ).
cnf(c_0_198,plain,
product(difference(c1,c),c1) = product(difference(bigA,b1),bigA),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_184]),c_0_185]) ).
cnf(c_0_199,plain,
quotient(product(a1,product(X1,b1)),c) = product(b1,X1),
inference(spm,[status(thm)],[c_0_54,c_0_60]) ).
cnf(c_0_200,plain,
product(a1,product(difference(b,X1),b)) = product(X1,c1),
inference(spm,[status(thm)],[c_0_68,c_0_27]) ).
cnf(c_0_201,plain,
product(difference(b,c),b) = bigA,
inference(spm,[status(thm)],[c_0_88,c_0_121]) ).
cnf(c_0_202,plain,
quotient(a,b) = difference(b,bigC),
inference(spm,[status(thm)],[c_0_28,c_0_186]) ).
cnf(c_0_203,plain,
difference(bigC,product(b,a)) = product(difference(bigC,a),bigC),
inference(spm,[status(thm)],[c_0_33,c_0_92]) ).
cnf(c_0_204,plain,
quotient(product(a,c),bigB) = c,
inference(rw,[status(thm)],[c_0_187,c_0_105]) ).
cnf(c_0_205,plain,
difference(bigB,product(a,c)) = a,
inference(spm,[status(thm)],[c_0_28,c_0_47]) ).
cnf(c_0_206,plain,
quotient(product(c1,X1),b) = product(a1,quotient(X1,a1)),
inference(spm,[status(thm)],[c_0_188,c_0_88]) ).
cnf(c_0_207,plain,
product(c1,difference(bigB,a1)) = product(b,a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_190]),c_0_191]),c_0_136]) ).
cnf(c_0_208,plain,
product(X1,product(X1,quotient(X2,X1))) = difference(product(X2,X1),X1),
inference(spm,[status(thm)],[c_0_192,c_0_88]) ).
cnf(c_0_209,plain,
product(product(c,c1),c1) = product(c1,product(a,bigA)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_48]),c_0_194]) ).
cnf(c_0_210,plain,
product(difference(bigA,b1),bigA) = quotient(b1,bigC),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_196]),c_0_197]),c_0_198]) ).
cnf(c_0_211,plain,
quotient(product(a,product(X1,b1)),c1) = product(b1,X1),
inference(spm,[status(thm)],[c_0_54,c_0_53]) ).
cnf(c_0_212,plain,
quotient(product(a1,X1),c) = product(b1,quotient(X1,b1)),
inference(spm,[status(thm)],[c_0_199,c_0_88]) ).
cnf(c_0_213,plain,
product(a1,bigA) = product(c,c1),
inference(spm,[status(thm)],[c_0_200,c_0_201]) ).
cnf(c_0_214,plain,
product(difference(bigC,a),bigC) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_202]),c_0_27]),c_0_203]) ).
cnf(c_0_215,plain,
product(difference(bigB,c),bigB) = a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_204]),c_0_205]) ).
cnf(c_0_216,plain,
product(a1,quotient(difference(bigB,a1),a1)) = bigC,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_207]),c_0_103]),c_0_202]),c_0_27]) ).
cnf(c_0_217,plain,
difference(difference(X1,X2),difference(product(X1,X2),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_208]),c_0_103]),c_0_208]),c_0_88]) ).
cnf(c_0_218,plain,
product(quotient(b1,bigC),c1) = product(a,bigA),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_209]),c_0_28]),c_0_33]),c_0_198]),c_0_210]) ).
cnf(c_0_219,plain,
quotient(product(a,X1),c1) = product(b1,quotient(X1,b1)),
inference(spm,[status(thm)],[c_0_211,c_0_88]) ).
cnf(c_0_220,plain,
product(b1,quotient(bigA,b1)) = product(c,quotient(c1,c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_213]),c_0_103]) ).
cnf(c_0_221,plain,
quotient(quotient(X1,product(X1,X2)),quotient(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_178]),c_0_33]),c_0_178]),c_0_27]) ).
cnf(c_0_222,plain,
product(product(bigC,X1),b) = product(a,product(X1,bigC)),
inference(spm,[status(thm)],[c_0_43,c_0_214]) ).
cnf(c_0_223,plain,
product(product(bigB,X1),a) = product(c,product(X1,bigB)),
inference(spm,[status(thm)],[c_0_43,c_0_215]) ).
cnf(c_0_224,plain,
quotient(difference(bigB,a1),a1) = difference(a1,bigC),
inference(spm,[status(thm)],[c_0_28,c_0_216]) ).
cnf(c_0_225,plain,
difference(product(X1,X2),X2) = product(difference(X1,X2),X2),
inference(spm,[status(thm)],[c_0_27,c_0_217]) ).
cnf(c_0_226,plain,
product(c,quotient(c1,c)) = quotient(b1,bigC),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_218]),c_0_219]),c_0_220]) ).
cnf(c_0_227,plain,
quotient(product(c,a),quotient(b1,bigC)) = b1,
inference(spm,[status(thm)],[c_0_221,c_0_196]) ).
cnf(c_0_228,plain,
quotient(product(a,product(X1,bigC)),b) = product(bigC,X1),
inference(spm,[status(thm)],[c_0_54,c_0_222]) ).
cnf(c_0_229,plain,
difference(product(bigB,X1),product(c,product(X1,bigB))) = a,
inference(spm,[status(thm)],[c_0_28,c_0_223]) ).
cnf(c_0_230,plain,
product(c,product(difference(a1,X1),a1)) = product(X1,b1),
inference(spm,[status(thm)],[c_0_176,c_0_27]) ).
cnf(c_0_231,plain,
product(difference(a1,bigC),a1) = difference(bigB,a1),
inference(spm,[status(thm)],[c_0_88,c_0_224]) ).
cnf(c_0_232,plain,
product(difference(b,bigC),b) = a,
inference(spm,[status(thm)],[c_0_88,c_0_202]) ).
cnf(c_0_233,plain,
product(X1,product(X1,quotient(X2,X1))) = product(difference(X2,X1),X1),
inference(rw,[status(thm)],[c_0_208,c_0_225]) ).
cnf(c_0_234,plain,
product(b1,quotient(bigA,b1)) = quotient(b1,bigC),
inference(rw,[status(thm)],[c_0_220,c_0_226]) ).
cnf(c_0_235,plain,
product(b1,quotient(b1,bigC)) = product(c,a),
inference(spm,[status(thm)],[c_0_88,c_0_227]) ).
cnf(c_0_236,plain,
quotient(product(c,product(X1,a1)),b1) = product(a1,X1),
inference(spm,[status(thm)],[c_0_54,c_0_176]) ).
cnf(c_0_237,plain,
quotient(product(a,b1),b) = product(a1,quotient(a,a1)),
inference(spm,[status(thm)],[c_0_206,c_0_165]) ).
cnf(c_0_238,plain,
quotient(product(a,X1),b) = product(bigC,quotient(X1,bigC)),
inference(spm,[status(thm)],[c_0_228,c_0_88]) ).
cnf(c_0_239,plain,
difference(product(bigB,quotient(X1,bigB)),product(c,X1)) = a,
inference(spm,[status(thm)],[c_0_229,c_0_88]) ).
cnf(c_0_240,plain,
product(c,difference(bigB,a1)) = product(bigC,b1),
inference(spm,[status(thm)],[c_0_230,c_0_231]) ).
cnf(c_0_241,plain,
product(product(b,X1),a) = product(bigC,product(X1,b)),
inference(spm,[status(thm)],[c_0_43,c_0_232]) ).
cnf(c_0_242,plain,
product(product(b,c1),product(X1,b)) = product(c1,product(X1,a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_40]),c_0_172]) ).
cnf(c_0_243,plain,
product(bigC,b) = product(b,a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_214]),c_0_92]) ).
cnf(c_0_244,plain,
product(product(X1,X2),product(X1,X3)) = product(X1,product(X2,X3)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_245,plain,
product(difference(bigA,b1),b1) = product(c,a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_233,c_0_234]),c_0_235]) ).
cnf(c_0_246,plain,
quotient(product(c,X1),b1) = product(a1,quotient(X1,a1)),
inference(spm,[status(thm)],[c_0_236,c_0_88]) ).
cnf(c_0_247,plain,
product(a1,quotient(a,a1)) = product(bigC,quotient(b1,bigC)),
inference(rw,[status(thm)],[c_0_237,c_0_238]) ).
cnf(c_0_248,plain,
difference(quotient(a1,bigB),product(bigC,b1)) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_240]),c_0_147]),c_0_27]) ).
cnf(c_0_249,plain,
quotient(product(bigC,product(X1,b)),a) = product(b,X1),
inference(spm,[status(thm)],[c_0_54,c_0_241]) ).
cnf(c_0_250,plain,
product(product(X1,product(X2,X3)),product(X4,product(X5,X3))) = product(product(X1,X4),product(product(X2,X5),X3)),
inference(spm,[status(thm)],[c_0_18,c_0_21]) ).
cnf(c_0_251,plain,
quotient(product(b,product(X1,bigA)),c) = product(bigA,X1),
inference(spm,[status(thm)],[c_0_54,c_0_81]) ).
cnf(c_0_252,plain,
product(c1,product(bigC,a1)) = product(b,product(a,b1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_242,c_0_243]),c_0_244]),c_0_165]) ).
cnf(c_0_253,plain,
product(bigC,quotient(b1,bigC)) = difference(bigA,b1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_245]),c_0_246]),c_0_247]) ).
cnf(c_0_254,plain,
quotient(product(bigC,b1),a) = quotient(a1,bigB),
inference(spm,[status(thm)],[c_0_156,c_0_248]) ).
cnf(c_0_255,plain,
quotient(product(bigC,X1),a) = product(b,quotient(X1,b)),
inference(spm,[status(thm)],[c_0_249,c_0_88]) ).
cnf(c_0_256,plain,
product(product(X1,product(X2,X3)),product(product(X3,X4),X5)) = product(product(X1,product(X2,X4)),product(X3,X5)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_18]),c_0_250]) ).
cnf(c_0_257,plain,
product(product(X1,X2),product(X2,product(X3,X2))) = product(product(X1,product(X2,X3)),X2),
inference(spm,[status(thm)],[c_0_21,c_0_26]) ).
cnf(c_0_258,plain,
quotient(product(b,X1),c) = product(bigA,quotient(X1,bigA)),
inference(spm,[status(thm)],[c_0_251,c_0_88]) ).
cnf(c_0_259,plain,
product(b,difference(bigA,b1)) = product(a1,bigC),
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_252]),c_0_103]),c_0_238]),c_0_253]),c_0_54]) ).
cnf(c_0_260,plain,
product(product(b,X1),bigA) = product(c,product(X1,b)),
inference(spm,[status(thm)],[c_0_43,c_0_201]) ).
cnf(c_0_261,plain,
product(b,quotient(b1,b)) = quotient(a1,bigB),
inference(rw,[status(thm)],[c_0_254,c_0_255]) ).
cnf(c_0_262,plain,
product(c,product(difference(bigB,X1),bigB)) = product(X1,a),
inference(spm,[status(thm)],[c_0_223,c_0_27]) ).
cnf(c_0_263,plain,
product(product(product(X1,X2),product(X2,X1)),X2) = product(X2,product(product(X1,X2),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_45]),c_0_256]),c_0_19]),c_0_19]),c_0_257]) ).
cnf(c_0_264,plain,
product(product(X1,quotient(X2,X3)),X3) = product(product(X1,X3),X2),
inference(spm,[status(thm)],[c_0_21,c_0_88]) ).
cnf(c_0_265,plain,
product(b1,quotient(bigC,b1)) = quotient(b1,bigA),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_258,c_0_259]),c_0_212]),c_0_147]),c_0_27]) ).
cnf(c_0_266,plain,
product(quotient(a1,bigB),bigA) = product(c,b1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_260,c_0_261]),c_0_88]) ).
cnf(c_0_267,plain,
product(quotient(X1,bigB),a) = product(c,difference(bigB,X1)),
inference(spm,[status(thm)],[c_0_262,c_0_128]) ).
fof(c_0_268,negated_conjecture,
~ m(bigA,b1,bigC),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_269,plain,
! [X29,X30,X31] :
( ( m(X29,X30,X31)
| product(product(X29,X30),product(X30,X31)) != product(X29,X31) )
& ( product(product(X29,X30),product(X30,X31)) = product(X29,X31)
| ~ m(X29,X30,X31) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos09])])]) ).
cnf(c_0_270,plain,
product(product(difference(X1,X2),X1),X2) = product(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_263,c_0_128]),c_0_27]),c_0_264]),c_0_30]) ).
cnf(c_0_271,plain,
difference(b1,quotient(b1,bigA)) = quotient(bigC,b1),
inference(spm,[status(thm)],[c_0_28,c_0_265]) ).
cnf(c_0_272,plain,
product(quotient(b1,bigA),b1) = product(b1,bigC),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_265]),c_0_88]) ).
cnf(c_0_273,plain,
product(product(bigC,b1),product(bigA,bigC)) = b1,
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_163,c_0_266]),c_0_267]),c_0_240]),c_0_18]),c_0_151]),c_0_18]),c_0_166]) ).
fof(c_0_274,negated_conjecture,
~ m(bigA,b1,bigC),
inference(fof_simplification,[status(thm)],[c_0_268]) ).
cnf(c_0_275,plain,
( product(product(X1,X2),product(X2,X3)) != product(X1,X3)
| m(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_269]) ).
cnf(c_0_276,plain,
product(bigC,quotient(b1,bigA)) = product(b1,bigC),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_270,c_0_271]),c_0_88]),c_0_272]) ).
cnf(c_0_277,plain,
product(difference(bigC,b1),b1) = product(bigA,bigC),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_273]),c_0_225]) ).
fof(c_0_278,negated_conjecture,
~ m(bigA,b1,bigC),
inference(fof_nnf,[status(thm)],[c_0_274]) ).
cnf(c_0_279,plain,
( product(product(X1,X2),product(product(X2,X3),product(X3,X2))) != product(X1,X2)
| m(X1,product(X2,X3),X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_275,c_0_26]),c_0_18]) ).
cnf(c_0_280,plain,
product(difference(bigC,b1),bigC) = quotient(b1,bigA),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_276]),c_0_33]) ).
cnf(c_0_281,plain,
product(b1,quotient(b1,bigA)) = product(bigA,bigC),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_233,c_0_265]),c_0_277]) ).
cnf(c_0_282,negated_conjecture,
~ m(bigA,b1,bigC),
inference(split_conjunct,[status(thm)],[c_0_278]) ).
cnf(c_0_283,plain,
( product(product(X1,bigA),bigC) != product(X1,bigC)
| m(X1,b1,bigC) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_279,c_0_280]),c_0_27]),c_0_27]),c_0_281]),c_0_21]) ).
cnf(c_0_284,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_282,c_0_283]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP779+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/10.38 % Computer : n015.cluster.edu
% 0.11/10.38 % Model : x86_64 x86_64
% 0.11/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.38 % Memory : 8046.5625MB
% 0.11/10.38 % OS : Linux 6.8.0-71-generic
% 0.11/10.38 % CPULimit : 300
% 0.11/10.38 % WCLimit : 300
% 0.11/10.38 % DateTime : Sun Sep 20 20:43:16 UTC 2026
% 0.11/10.38 % CPUTime :
% 0.11/10.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/10.43 Running first-order theorem proving
% 0.15/10.43 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/benchmark/theBenchmark.p
% 78.79/20.49 % Version: 3.5.1
% 78.79/20.49 % Preprocessing class: FSMSSMSMSSSNFFN.
% 78.79/20.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 78.79/20.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 78.79/20.49 % Starting new_bool_3 with 300s (1) cores
% 78.79/20.49 % Starting new_bool_1 with 300s (1) cores
% 78.79/20.49 % Starting sh5l with 300s (1) cores
% 78.79/20.49 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 3900731 completed with status 0
% 78.79/20.49 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 78.79/20.49 % Preprocessing class: FSMSSMSMSSSNFFN.
% 78.79/20.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 78.79/20.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 78.79/20.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 78.79/20.49 % No SInE strategy applied
% 78.79/20.49 % Search class: FHUSM-FFSM22-MFFFFFNN
% 78.79/20.49 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 78.79/20.49 % Starting SubtermCWHack with 136s (1) cores
% 78.79/20.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 78.79/20.49 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 78.79/20.49 % Starting new_bool_3 with 136s (1) cores
% 78.79/20.49 % Starting new_bool_1 with 136s (1) cores
% 78.79/20.49 % G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with pid 3900739 completed with status 0
% 78.79/20.49 % Result found by G-E--_300_C18_F1_SE_CS_SP_PS_S0Y
% 78.79/20.49 % Preprocessing class: FSMSSMSMSSSNFFN.
% 78.79/20.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 78.79/20.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 78.79/20.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 78.79/20.49 % No SInE strategy applied
% 78.79/20.49 % Search class: FHUSM-FFSM22-MFFFFFNN
% 78.79/20.49 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 78.79/20.49 % Starting SubtermCWHack with 136s (1) cores
% 78.79/20.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 78.79/20.49 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 78.79/20.49 % Preprocessing time : 0.001 s
% 78.79/20.49 % Presaturation interreduction done
% 78.79/20.49
% 78.79/20.49 % Proof found!
% 78.79/20.49 % SZS status Theorem
% 78.79/20.49 % SZS output start CNFRefutation
% See solution above
% 78.79/20.49 % Parsed axioms : 16
% 78.79/20.49 % Removed by relevancy pruning/SinE : 0
% 78.79/20.49 % Initial clauses : 18
% 78.79/20.49 % Removed in clause preprocessing : 0
% 78.79/20.49 % Initial clauses in saturation : 18
% 78.79/20.49 % Processed clauses : 11475
% 78.79/20.49 % ...of these trivial : 2685
% 78.79/20.49 % ...subsumed : 3943
% 78.79/20.49 % ...remaining for further processing : 4847
% 78.79/20.49 % Other redundant clauses eliminated : 76
% 78.79/20.49 % Clauses deleted for lack of memory : 0
% 78.79/20.49 % Backward-subsumed : 410
% 78.79/20.49 % Backward-rewritten : 1106
% 78.79/20.49 % Generated clauses : 515619
% 78.79/20.49 % ...of the previous two non-redundant : 498462
% 78.79/20.49 % ...aggressively subsumed : 0
% 78.79/20.49 % Contextual simplify-reflections : 95
% 78.79/20.49 % Paramodulations : 515543
% 78.79/20.49 % Factorizations : 0
% 78.79/20.49 % NegExts : 0
% 78.79/20.49 % Equation resolutions : 76
% 78.79/20.49 % Disequality decompositions : 0
% 78.79/20.49 % Total rewrite steps : 316058
% 78.79/20.49 % ...of those cached : 288851
% 78.79/20.49 % Propositional unsat checks : 0
% 78.79/20.49 % Propositional check models : 0
% 78.79/20.49 % Propositional check unsatisfiable : 0
% 78.79/20.49 % Propositional clauses : 0
% 78.79/20.49 % Propositional clauses after purity: 0
% 78.79/20.49 % Propositional unsat core size : 0
% 78.79/20.49 % Propositional preprocessing time : 0.000
% 78.79/20.49 % Propositional encoding time : 0.000
% 78.79/20.49 % Propositional solver time : 0.000
% 78.79/20.49 % Success case prop preproc time : 0.000
% 78.79/20.49 % Success case prop encoding time : 0.000
% 78.79/20.49 % Success case prop solver time : 0.000
% 78.79/20.49 % Current number of processed clauses : 3313
% 78.79/20.49 % Positive orientable unit clauses : 2215
% 78.79/20.49 % Positive unorientable unit clauses: 15
% 78.79/20.49 % Negative unit clauses : 83
% 78.79/20.49 % Non-unit-clauses : 1000
% 78.79/20.49 % Current number of unprocessed clauses: 484312
% 78.79/20.49 % ...number of literals in the above : 806275
% 78.79/20.49 % Current number of archived formulas : 0
% 78.79/20.49 % Current number of archived clauses : 1534
% 78.79/20.49 % Clause-clause subsumption calls (NU) : 275916
% 78.79/20.49 % Rec. Clause-clause subsumption calls : 121203
% 78.79/20.49 % Non-unit clause-clause subsumptions : 3848
% 78.79/20.49 % Unit Clause-clause subsumption calls : 31351
% 78.79/20.49 % Rewrite failures with RHS unbound : 0
% 78.79/20.49 % BW rewrite match attempts : 2818
% 78.79/20.49 % BW rewrite match successes : 757
% 78.79/20.49 % Condensation attempts : 0
% 78.79/20.49 % Condensation successes : 0
% 78.79/20.49 % Termbank termtop insertions : 9891657
% 78.79/20.49 % Search garbage collected termcells : 46
% 78.79/20.49
% 78.79/20.49 % -------------------------------------------------
% 78.79/20.49 % User time : 9.406 s
% 78.79/20.49 % System time : 0.371 s
% 78.79/20.49 % Total time : 9.776 s
% 78.79/20.49 % Maximum resident set size: 3644 pages
% 78.79/20.49
% 78.79/20.49 % -------------------------------------------------
% 78.79/20.49 % User time : 47.168 s
% 78.79/20.49 % System time : 1.619 s
% 78.79/20.49 % Total time : 48.787 s
% 78.79/20.49 % Maximum resident set size: 4864 pages
% 78.79/20.49 % E exiting
%------------------------------------------------------------------------------