TSTP Solution File: KLE099+1 by SRASS---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SRASS---0.1
% Problem : KLE099+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : SRASS -q2 -a 0 10 10 10 -i3 -n60 %s
% Computer : art01.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Wed Dec 29 07:56:17 EST 2010
% Result : Theorem 4.36s
% Output : Solution 4.36s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Reading problem from /tmp/SystemOnTPTP5337/KLE099+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM ...
% found
% SZS status THM for /tmp/SystemOnTPTP5337/KLE099+1.tptp
% SZS output start Solution for /tmp/SystemOnTPTP5337/KLE099+1.tptp
% TreeLimitedRun: ----------------------------------------------------------
% TreeLimitedRun: /home/graph/tptp/Systems/EP---1.2/eproof --print-statistics -xAuto -tAuto --cpu-limit=60 --proof-time-unlimited --memory-limit=Auto --tstp-in --tstp-out /tmp/SRASS.s.p
% TreeLimitedRun: CPU time limit is 60s
% TreeLimitedRun: WC time limit is 120s
% TreeLimitedRun: PID is 5433
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.02 WC
% # Preprocessing time : 0.012 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% PrfWatch: 1.93 CPU 2.03 WC
% # SZS output start CNFRefutation.
% fof(1, axiom,![X1]:![X2]:addition(X1,X2)=addition(X2,X1),file('/tmp/SRASS.s.p', additive_commutativity)).
% fof(2, axiom,![X3]:![X2]:![X1]:addition(X1,addition(X2,X3))=addition(addition(X1,X2),X3),file('/tmp/SRASS.s.p', additive_associativity)).
% fof(3, axiom,![X1]:addition(X1,zero)=X1,file('/tmp/SRASS.s.p', additive_identity)).
% fof(4, axiom,![X1]:addition(X1,X1)=X1,file('/tmp/SRASS.s.p', additive_idempotence)).
% fof(5, axiom,![X1]:![X2]:![X3]:multiplication(X1,multiplication(X2,X3))=multiplication(multiplication(X1,X2),X3),file('/tmp/SRASS.s.p', multiplicative_associativity)).
% fof(6, axiom,![X1]:![X2]:![X3]:multiplication(X1,addition(X2,X3))=addition(multiplication(X1,X2),multiplication(X1,X3)),file('/tmp/SRASS.s.p', right_distributivity)).
% fof(7, axiom,![X1]:![X2]:![X3]:multiplication(addition(X1,X2),X3)=addition(multiplication(X1,X3),multiplication(X2,X3)),file('/tmp/SRASS.s.p', left_distributivity)).
% fof(8, axiom,![X1]:multiplication(X1,zero)=zero,file('/tmp/SRASS.s.p', right_annihilation)).
% fof(9, axiom,![X1]:multiplication(zero,X1)=zero,file('/tmp/SRASS.s.p', left_annihilation)).
% fof(10, axiom,![X4]:multiplication(antidomain(X4),X4)=zero,file('/tmp/SRASS.s.p', domain1)).
% fof(11, axiom,![X4]:![X5]:addition(antidomain(multiplication(X4,X5)),antidomain(multiplication(X4,antidomain(antidomain(X5)))))=antidomain(multiplication(X4,antidomain(antidomain(X5)))),file('/tmp/SRASS.s.p', domain2)).
% fof(12, axiom,![X4]:domain(X4)=antidomain(antidomain(X4)),file('/tmp/SRASS.s.p', domain4)).
% fof(13, axiom,![X4]:![X5]:forward_diamond(X4,X5)=domain(multiplication(X4,domain(X5))),file('/tmp/SRASS.s.p', forward_diamond)).
% fof(16, axiom,![X4]:addition(antidomain(antidomain(X4)),antidomain(X4))=one,file('/tmp/SRASS.s.p', domain3)).
% fof(17, axiom,![X4]:multiplication(X4,coantidomain(X4))=zero,file('/tmp/SRASS.s.p', codomain1)).
% fof(18, axiom,![X4]:![X5]:addition(coantidomain(multiplication(X4,X5)),coantidomain(multiplication(coantidomain(coantidomain(X4)),X5)))=coantidomain(multiplication(coantidomain(coantidomain(X4)),X5)),file('/tmp/SRASS.s.p', codomain2)).
% fof(19, axiom,![X1]:![X2]:(leq(X1,X2)<=>addition(X1,X2)=X2),file('/tmp/SRASS.s.p', order)).
% fof(21, axiom,![X1]:multiplication(X1,one)=X1,file('/tmp/SRASS.s.p', multiplicative_right_identity)).
% fof(22, axiom,![X1]:multiplication(one,X1)=X1,file('/tmp/SRASS.s.p', multiplicative_left_identity)).
% fof(23, axiom,![X4]:addition(coantidomain(coantidomain(X4)),coantidomain(X4))=one,file('/tmp/SRASS.s.p', codomain3)).
% fof(27, conjecture,![X4]:![X5]:![X6]:(addition(forward_diamond(X4,domain(X5)),domain(X6))=domain(X6)=>multiplication(antidomain(X6),multiplication(X4,domain(X5)))=zero),file('/tmp/SRASS.s.p', goals)).
% fof(28, negated_conjecture,~(![X4]:![X5]:![X6]:(addition(forward_diamond(X4,domain(X5)),domain(X6))=domain(X6)=>multiplication(antidomain(X6),multiplication(X4,domain(X5)))=zero)),inference(assume_negation,[status(cth)],[27])).
% fof(29, plain,![X3]:![X4]:addition(X3,X4)=addition(X4,X3),inference(variable_rename,[status(thm)],[1])).
% cnf(30,plain,(addition(X1,X2)=addition(X2,X1)),inference(split_conjunct,[status(thm)],[29])).
% fof(31, plain,![X4]:![X5]:![X6]:addition(X6,addition(X5,X4))=addition(addition(X6,X5),X4),inference(variable_rename,[status(thm)],[2])).
% cnf(32,plain,(addition(X1,addition(X2,X3))=addition(addition(X1,X2),X3)),inference(split_conjunct,[status(thm)],[31])).
% fof(33, plain,![X2]:addition(X2,zero)=X2,inference(variable_rename,[status(thm)],[3])).
% cnf(34,plain,(addition(X1,zero)=X1),inference(split_conjunct,[status(thm)],[33])).
% fof(35, plain,![X2]:addition(X2,X2)=X2,inference(variable_rename,[status(thm)],[4])).
% cnf(36,plain,(addition(X1,X1)=X1),inference(split_conjunct,[status(thm)],[35])).
% fof(37, plain,![X4]:![X5]:![X6]:multiplication(X4,multiplication(X5,X6))=multiplication(multiplication(X4,X5),X6),inference(variable_rename,[status(thm)],[5])).
% cnf(38,plain,(multiplication(X1,multiplication(X2,X3))=multiplication(multiplication(X1,X2),X3)),inference(split_conjunct,[status(thm)],[37])).
% fof(39, plain,![X4]:![X5]:![X6]:multiplication(X4,addition(X5,X6))=addition(multiplication(X4,X5),multiplication(X4,X6)),inference(variable_rename,[status(thm)],[6])).
% cnf(40,plain,(multiplication(X1,addition(X2,X3))=addition(multiplication(X1,X2),multiplication(X1,X3))),inference(split_conjunct,[status(thm)],[39])).
% fof(41, plain,![X4]:![X5]:![X6]:multiplication(addition(X4,X5),X6)=addition(multiplication(X4,X6),multiplication(X5,X6)),inference(variable_rename,[status(thm)],[7])).
% cnf(42,plain,(multiplication(addition(X1,X2),X3)=addition(multiplication(X1,X3),multiplication(X2,X3))),inference(split_conjunct,[status(thm)],[41])).
% fof(43, plain,![X2]:multiplication(X2,zero)=zero,inference(variable_rename,[status(thm)],[8])).
% cnf(44,plain,(multiplication(X1,zero)=zero),inference(split_conjunct,[status(thm)],[43])).
% fof(45, plain,![X2]:multiplication(zero,X2)=zero,inference(variable_rename,[status(thm)],[9])).
% cnf(46,plain,(multiplication(zero,X1)=zero),inference(split_conjunct,[status(thm)],[45])).
% fof(47, plain,![X5]:multiplication(antidomain(X5),X5)=zero,inference(variable_rename,[status(thm)],[10])).
% cnf(48,plain,(multiplication(antidomain(X1),X1)=zero),inference(split_conjunct,[status(thm)],[47])).
% fof(49, plain,![X6]:![X7]:addition(antidomain(multiplication(X6,X7)),antidomain(multiplication(X6,antidomain(antidomain(X7)))))=antidomain(multiplication(X6,antidomain(antidomain(X7)))),inference(variable_rename,[status(thm)],[11])).
% cnf(50,plain,(addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2)))))=antidomain(multiplication(X1,antidomain(antidomain(X2))))),inference(split_conjunct,[status(thm)],[49])).
% fof(51, plain,![X5]:domain(X5)=antidomain(antidomain(X5)),inference(variable_rename,[status(thm)],[12])).
% cnf(52,plain,(domain(X1)=antidomain(antidomain(X1))),inference(split_conjunct,[status(thm)],[51])).
% fof(53, plain,![X6]:![X7]:forward_diamond(X6,X7)=domain(multiplication(X6,domain(X7))),inference(variable_rename,[status(thm)],[13])).
% cnf(54,plain,(forward_diamond(X1,X2)=domain(multiplication(X1,domain(X2)))),inference(split_conjunct,[status(thm)],[53])).
% fof(59, plain,![X5]:addition(antidomain(antidomain(X5)),antidomain(X5))=one,inference(variable_rename,[status(thm)],[16])).
% cnf(60,plain,(addition(antidomain(antidomain(X1)),antidomain(X1))=one),inference(split_conjunct,[status(thm)],[59])).
% fof(61, plain,![X5]:multiplication(X5,coantidomain(X5))=zero,inference(variable_rename,[status(thm)],[17])).
% cnf(62,plain,(multiplication(X1,coantidomain(X1))=zero),inference(split_conjunct,[status(thm)],[61])).
% fof(63, plain,![X6]:![X7]:addition(coantidomain(multiplication(X6,X7)),coantidomain(multiplication(coantidomain(coantidomain(X6)),X7)))=coantidomain(multiplication(coantidomain(coantidomain(X6)),X7)),inference(variable_rename,[status(thm)],[18])).
% cnf(64,plain,(addition(coantidomain(multiplication(X1,X2)),coantidomain(multiplication(coantidomain(coantidomain(X1)),X2)))=coantidomain(multiplication(coantidomain(coantidomain(X1)),X2))),inference(split_conjunct,[status(thm)],[63])).
% fof(65, plain,![X1]:![X2]:((~(leq(X1,X2))|addition(X1,X2)=X2)&(~(addition(X1,X2)=X2)|leq(X1,X2))),inference(fof_nnf,[status(thm)],[19])).
% fof(66, plain,![X3]:![X4]:((~(leq(X3,X4))|addition(X3,X4)=X4)&(~(addition(X3,X4)=X4)|leq(X3,X4))),inference(variable_rename,[status(thm)],[65])).
% cnf(67,plain,(leq(X1,X2)|addition(X1,X2)!=X2),inference(split_conjunct,[status(thm)],[66])).
% cnf(68,plain,(addition(X1,X2)=X2|~leq(X1,X2)),inference(split_conjunct,[status(thm)],[66])).
% fof(71, plain,![X2]:multiplication(X2,one)=X2,inference(variable_rename,[status(thm)],[21])).
% cnf(72,plain,(multiplication(X1,one)=X1),inference(split_conjunct,[status(thm)],[71])).
% fof(73, plain,![X2]:multiplication(one,X2)=X2,inference(variable_rename,[status(thm)],[22])).
% cnf(74,plain,(multiplication(one,X1)=X1),inference(split_conjunct,[status(thm)],[73])).
% fof(75, plain,![X5]:addition(coantidomain(coantidomain(X5)),coantidomain(X5))=one,inference(variable_rename,[status(thm)],[23])).
% cnf(76,plain,(addition(coantidomain(coantidomain(X1)),coantidomain(X1))=one),inference(split_conjunct,[status(thm)],[75])).
% fof(83, negated_conjecture,?[X4]:?[X5]:?[X6]:(addition(forward_diamond(X4,domain(X5)),domain(X6))=domain(X6)&~(multiplication(antidomain(X6),multiplication(X4,domain(X5)))=zero)),inference(fof_nnf,[status(thm)],[28])).
% fof(84, negated_conjecture,?[X7]:?[X8]:?[X9]:(addition(forward_diamond(X7,domain(X8)),domain(X9))=domain(X9)&~(multiplication(antidomain(X9),multiplication(X7,domain(X8)))=zero)),inference(variable_rename,[status(thm)],[83])).
% fof(85, negated_conjecture,(addition(forward_diamond(esk1_0,domain(esk2_0)),domain(esk3_0))=domain(esk3_0)&~(multiplication(antidomain(esk3_0),multiplication(esk1_0,domain(esk2_0)))=zero)),inference(skolemize,[status(esa)],[84])).
% cnf(86,negated_conjecture,(multiplication(antidomain(esk3_0),multiplication(esk1_0,domain(esk2_0)))!=zero),inference(split_conjunct,[status(thm)],[85])).
% cnf(87,negated_conjecture,(addition(forward_diamond(esk1_0,domain(esk2_0)),domain(esk3_0))=domain(esk3_0)),inference(split_conjunct,[status(thm)],[85])).
% cnf(89,plain,(antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2)))))=forward_diamond(X1,X2)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[54,52,theory(equality)]),52,theory(equality)]),['unfolding']).
% cnf(91,negated_conjecture,(addition(forward_diamond(esk1_0,antidomain(antidomain(esk2_0))),antidomain(antidomain(esk3_0)))=antidomain(antidomain(esk3_0))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[87,52,theory(equality)]),52,theory(equality)]),52,theory(equality)]),['unfolding']).
% cnf(92,negated_conjecture,(multiplication(antidomain(esk3_0),multiplication(esk1_0,antidomain(antidomain(esk2_0))))!=zero),inference(rw,[status(thm)],[86,52,theory(equality)]),['unfolding']).
% cnf(97,negated_conjecture,(addition(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(esk2_0))))))),antidomain(antidomain(esk3_0)))=antidomain(antidomain(esk3_0))),inference(rw,[status(thm)],[91,89,theory(equality)]),['unfolding']).
% cnf(98,plain,(multiplication(X1,multiplication(X2,coantidomain(X2)))=multiplication(X2,coantidomain(X2))),inference(spm,[status(thm)],[44,62,theory(equality)])).
% cnf(100,plain,(multiplication(multiplication(X2,coantidomain(X2)),X1)=multiplication(X2,coantidomain(X2))),inference(spm,[status(thm)],[46,62,theory(equality)])).
% cnf(101,plain,(addition(X1,multiplication(X2,coantidomain(X2)))=X1),inference(spm,[status(thm)],[34,62,theory(equality)])).
% cnf(102,plain,(zero=coantidomain(one)),inference(spm,[status(thm)],[74,62,theory(equality)])).
% cnf(108,plain,(multiplication(multiplication(antidomain(X2),X2),X1)=multiplication(antidomain(X2),X2)),inference(spm,[status(thm)],[46,48,theory(equality)])).
% cnf(110,plain,(zero=antidomain(one)),inference(spm,[status(thm)],[72,48,theory(equality)])).
% cnf(136,plain,(addition(X1,X2)=addition(X1,addition(X1,X2))),inference(spm,[status(thm)],[32,36,theory(equality)])).
% cnf(151,plain,(multiplication(X1,multiplication(X2,coantidomain(multiplication(X1,X2))))=zero),inference(spm,[status(thm)],[62,38,theory(equality)])).
% cnf(203,plain,(addition(zero,X1)=X1),inference(spm,[status(thm)],[34,30,theory(equality)])).
% cnf(206,plain,(leq(X1,X2)|addition(X2,X1)!=X2),inference(spm,[status(thm)],[67,30,theory(equality)])).
% cnf(207,plain,(addition(addition(X2,X1),X3)=addition(X1,addition(X2,X3))),inference(spm,[status(thm)],[32,30,theory(equality)])).
% cnf(222,plain,(addition(X2,addition(X1,X3))=addition(X1,addition(X2,X3))),inference(rw,[status(thm)],[207,32,theory(equality)])).
% cnf(234,plain,(addition(multiplication(X2,coantidomain(X2)),X1)=X1),inference(spm,[status(thm)],[203,62,theory(equality)])).
% cnf(280,plain,(addition(antidomain(X1),antidomain(antidomain(X1)))=one),inference(rw,[status(thm)],[60,30,theory(equality)])).
% cnf(291,plain,(addition(zero,antidomain(zero))=one),inference(spm,[status(thm)],[280,110,theory(equality)])).
% cnf(293,plain,(antidomain(zero)=one),inference(rw,[status(thm)],[291,203,theory(equality)])).
% cnf(295,plain,(antidomain(antidomain(zero))=zero),inference(rw,[status(thm)],[110,293,theory(equality)])).
% cnf(296,plain,(coantidomain(antidomain(zero))=zero),inference(rw,[status(thm)],[102,293,theory(equality)])).
% cnf(297,plain,(addition(antidomain(X1),antidomain(antidomain(X1)))=antidomain(zero)),inference(rw,[status(thm)],[280,293,theory(equality)])).
% cnf(298,plain,(multiplication(X1,antidomain(zero))=X1),inference(rw,[status(thm)],[72,293,theory(equality)])).
% cnf(299,plain,(multiplication(antidomain(zero),X1)=X1),inference(rw,[status(thm)],[74,293,theory(equality)])).
% cnf(301,plain,(leq(X1,addition(X2,X3))|addition(X2,addition(X3,X1))!=addition(X2,X3)),inference(spm,[status(thm)],[206,32,theory(equality)])).
% cnf(397,plain,(addition(coantidomain(X1),coantidomain(coantidomain(X1)))=one),inference(rw,[status(thm)],[76,30,theory(equality)])).
% cnf(398,plain,(addition(coantidomain(X1),coantidomain(coantidomain(X1)))=antidomain(zero)),inference(rw,[status(thm)],[397,293,theory(equality)])).
% cnf(418,plain,(addition(zero,coantidomain(zero))=antidomain(zero)),inference(spm,[status(thm)],[398,296,theory(equality)])).
% cnf(424,plain,(coantidomain(zero)=antidomain(zero)),inference(rw,[status(thm)],[418,203,theory(equality)])).
% cnf(430,plain,(antidomain(multiplication(X1,coantidomain(X1)))=coantidomain(multiplication(X1,coantidomain(X1)))),inference(spm,[status(thm)],[424,62,theory(equality)])).
% cnf(432,plain,(antidomain(coantidomain(zero))=zero),inference(rw,[status(thm)],[295,424,theory(equality)])).
% cnf(434,plain,(addition(coantidomain(X1),coantidomain(coantidomain(X1)))=coantidomain(zero)),inference(rw,[status(thm)],[398,424,theory(equality)])).
% cnf(435,plain,(multiplication(X1,coantidomain(zero))=X1),inference(rw,[status(thm)],[298,424,theory(equality)])).
% cnf(436,plain,(multiplication(coantidomain(zero),X1)=X1),inference(rw,[status(thm)],[299,424,theory(equality)])).
% cnf(445,plain,(antidomain(coantidomain(multiplication(X1,coantidomain(X1))))=multiplication(X1,coantidomain(X1))),inference(spm,[status(thm)],[432,62,theory(equality)])).
% cnf(463,plain,(multiplication(X1,coantidomain(multiplication(X2,coantidomain(X2))))=X1),inference(spm,[status(thm)],[435,62,theory(equality)])).
% cnf(979,plain,(addition(multiplication(X1,coantidomain(addition(X1,X2))),multiplication(X2,coantidomain(addition(X1,X2))))=zero),inference(spm,[status(thm)],[62,42,theory(equality)])).
% cnf(1032,plain,(addition(antidomain(X1),antidomain(antidomain(X1)))=coantidomain(zero)),inference(rw,[status(thm)],[297,424,theory(equality)])).
% cnf(1042,plain,(multiplication(addition(antidomain(X2),antidomain(antidomain(X2))),X1)=X1),inference(spm,[status(thm)],[436,1032,theory(equality)])).
% cnf(1043,plain,(multiplication(X1,addition(antidomain(X2),antidomain(antidomain(X2))))=X1),inference(spm,[status(thm)],[435,1032,theory(equality)])).
% cnf(1050,plain,(addition(antidomain(X1),coantidomain(zero))=coantidomain(zero)),inference(spm,[status(thm)],[136,1032,theory(equality)])).
% cnf(1089,plain,(addition(multiplication(antidomain(X2),X1),multiplication(antidomain(antidomain(X2)),X1))=X1),inference(rw,[status(thm)],[1042,42,theory(equality)])).
% cnf(1090,plain,(addition(multiplication(X1,antidomain(X2)),multiplication(X1,antidomain(antidomain(X2))))=X1),inference(rw,[status(thm)],[1043,40,theory(equality)])).
% cnf(1139,plain,(coantidomain(zero)=addition(coantidomain(zero),antidomain(X1))),inference(spm,[status(thm)],[30,1050,theory(equality)])).
% cnf(1142,plain,(multiplication(coantidomain(zero),X2)=addition(multiplication(antidomain(X1),X2),multiplication(coantidomain(zero),X2))),inference(spm,[status(thm)],[42,1050,theory(equality)])).
% cnf(1166,plain,(X2=addition(multiplication(antidomain(X1),X2),multiplication(coantidomain(zero),X2))),inference(rw,[status(thm)],[1142,436,theory(equality)])).
% cnf(1167,plain,(X2=addition(multiplication(antidomain(X1),X2),X2)),inference(rw,[status(thm)],[1166,436,theory(equality)])).
% cnf(1218,plain,(addition(coantidomain(multiplication(X2,coantidomain(X2))),antidomain(X1))=coantidomain(multiplication(X2,coantidomain(X2)))),inference(spm,[status(thm)],[1139,62,theory(equality)])).
% cnf(1275,plain,(addition(antidomain(zero),antidomain(multiplication(X1,antidomain(antidomain(coantidomain(X1))))))=antidomain(multiplication(X1,antidomain(antidomain(coantidomain(X1)))))),inference(spm,[status(thm)],[50,62,theory(equality)])).
% cnf(1317,plain,(coantidomain(zero)=antidomain(multiplication(X1,antidomain(antidomain(coantidomain(X1)))))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[1275,424,theory(equality)]),1139,theory(equality)])).
% cnf(1364,plain,(multiplication(X2,multiplication(coantidomain(X2),X1))=multiplication(X2,coantidomain(X2))),inference(rw,[status(thm)],[100,38,theory(equality)])).
% cnf(1371,plain,(addition(antidomain(multiplication(X1,coantidomain(X1))),antidomain(multiplication(X1,antidomain(antidomain(multiplication(coantidomain(X1),X2))))))=antidomain(multiplication(X1,antidomain(antidomain(multiplication(coantidomain(X1),X2)))))),inference(spm,[status(thm)],[50,1364,theory(equality)])).
% cnf(1373,plain,(multiplication(X1,coantidomain(X1))=multiplication(coantidomain(X1),coantidomain(coantidomain(X1)))),inference(spm,[status(thm)],[98,1364,theory(equality)])).
% cnf(1392,plain,(addition(coantidomain(multiplication(X1,coantidomain(X1))),antidomain(multiplication(X1,antidomain(antidomain(multiplication(coantidomain(X1),X2))))))=antidomain(multiplication(X1,antidomain(antidomain(multiplication(coantidomain(X1),X2)))))),inference(rw,[status(thm)],[1371,430,theory(equality)])).
% cnf(1525,plain,(multiplication(antidomain(X2),multiplication(X2,X1))=multiplication(antidomain(X2),X2)),inference(rw,[status(thm)],[108,38,theory(equality)])).
% cnf(1530,plain,(multiplication(antidomain(X1),X1)=multiplication(X1,coantidomain(X1))),inference(spm,[status(thm)],[98,1525,theory(equality)])).
% cnf(1581,plain,(multiplication(addition(X1,X2),coantidomain(addition(X1,X2)))=addition(multiplication(antidomain(addition(X1,X2)),X1),multiplication(antidomain(addition(X1,X2)),X2))),inference(spm,[status(thm)],[40,1530,theory(equality)])).
% cnf(1601,plain,(multiplication(antidomain(X1),multiplication(X1,X2))=multiplication(X1,coantidomain(X1))),inference(rw,[status(thm)],[1525,1530,theory(equality)])).
% cnf(1609,plain,(addition(multiplication(X1,coantidomain(addition(X1,X2))),multiplication(X2,coantidomain(addition(X1,X2))))=addition(multiplication(antidomain(addition(X1,X2)),X1),multiplication(antidomain(addition(X1,X2)),X2))),inference(rw,[status(thm)],[1581,42,theory(equality)])).
% cnf(1651,plain,(addition(coantidomain(multiplication(X1,multiplication(X2,X3))),coantidomain(multiplication(coantidomain(coantidomain(multiplication(X1,X2))),X3)))=coantidomain(multiplication(coantidomain(coantidomain(multiplication(X1,X2))),X3))),inference(spm,[status(thm)],[64,38,theory(equality)])).
% cnf(1727,plain,(multiplication(addition(coantidomain(X2),coantidomain(coantidomain(X2))),X1)=X1),inference(spm,[status(thm)],[436,434,theory(equality)])).
% cnf(1728,plain,(multiplication(X1,addition(coantidomain(X2),coantidomain(coantidomain(X2))))=X1),inference(spm,[status(thm)],[435,434,theory(equality)])).
% cnf(1740,plain,(addition(coantidomain(X1),coantidomain(zero))=coantidomain(zero)),inference(spm,[status(thm)],[136,434,theory(equality)])).
% cnf(1780,plain,(addition(multiplication(coantidomain(X2),X1),multiplication(coantidomain(coantidomain(X2)),X1))=X1),inference(rw,[status(thm)],[1727,42,theory(equality)])).
% cnf(1781,plain,(addition(multiplication(X1,coantidomain(X2)),multiplication(X1,coantidomain(coantidomain(X2))))=X1),inference(rw,[status(thm)],[1728,40,theory(equality)])).
% cnf(1860,plain,(coantidomain(zero)=addition(coantidomain(zero),coantidomain(X1))),inference(spm,[status(thm)],[30,1740,theory(equality)])).
% cnf(1863,plain,(multiplication(coantidomain(zero),X2)=addition(multiplication(coantidomain(X1),X2),multiplication(coantidomain(zero),X2))),inference(spm,[status(thm)],[42,1740,theory(equality)])).
% cnf(1875,plain,(multiplication(X1,coantidomain(zero))=addition(multiplication(X1,coantidomain(X2)),multiplication(X1,coantidomain(zero)))),inference(spm,[status(thm)],[40,1740,theory(equality)])).
% cnf(1887,plain,(X2=addition(multiplication(coantidomain(X1),X2),multiplication(coantidomain(zero),X2))),inference(rw,[status(thm)],[1863,436,theory(equality)])).
% cnf(1888,plain,(X2=addition(multiplication(coantidomain(X1),X2),X2)),inference(rw,[status(thm)],[1887,436,theory(equality)])).
% cnf(1894,plain,(X1=addition(multiplication(X1,coantidomain(X2)),multiplication(X1,coantidomain(zero)))),inference(rw,[status(thm)],[1875,435,theory(equality)])).
% cnf(1895,plain,(X1=addition(multiplication(X1,coantidomain(X2)),X1)),inference(rw,[status(thm)],[1894,435,theory(equality)])).
% cnf(1924,plain,(addition(coantidomain(multiplication(X2,coantidomain(X2))),coantidomain(X1))=coantidomain(multiplication(X2,coantidomain(X2)))),inference(spm,[status(thm)],[1860,62,theory(equality)])).
% cnf(2091,plain,(addition(X2,multiplication(antidomain(X1),X2))=X2),inference(rw,[status(thm)],[1167,30,theory(equality)])).
% cnf(2103,plain,(leq(multiplication(antidomain(X1),X2),X2)),inference(spm,[status(thm)],[206,2091,theory(equality)])).
% cnf(2814,plain,(addition(X2,multiplication(coantidomain(X1),X2))=X2),inference(rw,[status(thm)],[1888,30,theory(equality)])).
% cnf(2975,plain,(addition(X1,multiplication(X1,coantidomain(X2)))=X1),inference(rw,[status(thm)],[1895,30,theory(equality)])).
% cnf(5920,plain,(leq(multiplication(X1,coantidomain(X2)),addition(X3,X1))),inference(spm,[status(thm)],[301,2975,theory(equality)])).
% cnf(5949,plain,(leq(X1,addition(X2,X3))|addition(X3,addition(X2,X1))!=addition(X2,X3)),inference(spm,[status(thm)],[301,222,theory(equality)])).
% cnf(10049,plain,(coantidomain(multiplication(X1,coantidomain(X1)))=coantidomain(multiplication(coantidomain(coantidomain(X1)),coantidomain(X1)))),inference(spm,[status(thm)],[64,1924,theory(equality)])).
% cnf(10155,plain,(antidomain(coantidomain(multiplication(multiplication(coantidomain(coantidomain(X1)),coantidomain(X1)),coantidomain(multiplication(X1,coantidomain(X1))))))=multiplication(multiplication(coantidomain(coantidomain(X1)),coantidomain(X1)),coantidomain(multiplication(X1,coantidomain(X1))))),inference(spm,[status(thm)],[445,10049,theory(equality)])).
% cnf(10241,plain,(multiplication(X1,coantidomain(X1))=multiplication(multiplication(coantidomain(coantidomain(X1)),coantidomain(X1)),coantidomain(multiplication(X1,coantidomain(X1))))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[10155,38,theory(equality)]),463,theory(equality)]),10049,theory(equality)]),445,theory(equality)])).
% cnf(10242,plain,(multiplication(X1,coantidomain(X1))=multiplication(coantidomain(coantidomain(X1)),coantidomain(X1))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[10241,38,theory(equality)]),463,theory(equality)])).
% cnf(10346,plain,(addition(antidomain(multiplication(X1,coantidomain(X1))),antidomain(multiplication(coantidomain(coantidomain(X1)),antidomain(antidomain(coantidomain(X1))))))=antidomain(multiplication(coantidomain(coantidomain(X1)),antidomain(antidomain(coantidomain(X1)))))),inference(spm,[status(thm)],[50,10242,theory(equality)])).
% cnf(10379,plain,(coantidomain(multiplication(X1,coantidomain(X1)))=antidomain(multiplication(coantidomain(coantidomain(X1)),antidomain(antidomain(coantidomain(X1)))))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[10346,430,theory(equality)]),1218,theory(equality)])).
% cnf(15438,plain,(leq(multiplication(X1,coantidomain(X2)),addition(X1,X3))),inference(spm,[status(thm)],[5920,30,theory(equality)])).
% cnf(29094,plain,(addition(multiplication(X1,coantidomain(addition(X1,X2))),zero)=zero),inference(spm,[status(thm)],[136,979,theory(equality)])).
% cnf(29332,plain,(multiplication(X1,coantidomain(addition(X1,X2)))=zero),inference(rw,[status(thm)],[29094,34,theory(equality)])).
% cnf(42099,plain,(coantidomain(antidomain(antidomain(X1)))=multiplication(antidomain(X1),coantidomain(antidomain(antidomain(X1))))),inference(spm,[status(thm)],[101,1089,theory(equality)])).
% cnf(42194,plain,(addition(multiplication(X1,coantidomain(X1)),multiplication(antidomain(antidomain(X1)),multiplication(X1,X2)))=multiplication(X1,X2)),inference(spm,[status(thm)],[1089,1601,theory(equality)])).
% cnf(42195,plain,(addition(multiplication(X1,coantidomain(X1)),multiplication(antidomain(antidomain(X1)),X1))=X1),inference(spm,[status(thm)],[1089,1530,theory(equality)])).
% cnf(42319,plain,(multiplication(antidomain(antidomain(X1)),multiplication(X1,X2))=multiplication(X1,X2)),inference(rw,[status(thm)],[42194,234,theory(equality)])).
% cnf(42320,plain,(multiplication(antidomain(antidomain(X1)),X1)=X1),inference(rw,[status(thm)],[42195,234,theory(equality)])).
% cnf(42379,plain,(multiplication(antidomain(coantidomain(multiplication(X1,coantidomain(X1)))),multiplication(coantidomain(coantidomain(X1)),antidomain(antidomain(coantidomain(X1)))))=multiplication(coantidomain(coantidomain(X1)),antidomain(antidomain(coantidomain(X1))))),inference(spm,[status(thm)],[42320,10379,theory(equality)])).
% cnf(42384,plain,(multiplication(antidomain(coantidomain(zero)),multiplication(X1,antidomain(antidomain(coantidomain(X1)))))=multiplication(X1,antidomain(antidomain(coantidomain(X1))))),inference(spm,[status(thm)],[42320,1317,theory(equality)])).
% cnf(42438,plain,(multiplication(X1,coantidomain(X1))=multiplication(coantidomain(coantidomain(X1)),antidomain(antidomain(coantidomain(X1))))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[42379,445,theory(equality)]),38,theory(equality)]),1364,theory(equality)]),1373,theory(equality)]),98,theory(equality)])).
% cnf(42442,plain,(zero=multiplication(X1,antidomain(antidomain(coantidomain(X1))))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[42384,432,theory(equality)]),46,theory(equality)])).
% cnf(42697,plain,(leq(coantidomain(antidomain(antidomain(X1))),addition(antidomain(X1),X2))),inference(spm,[status(thm)],[15438,42099,theory(equality)])).
% cnf(43145,plain,(addition(multiplication(antidomain(antidomain(antidomain(X1))),antidomain(X1)),multiplication(antidomain(antidomain(X1)),coantidomain(antidomain(antidomain(X1)))))=antidomain(antidomain(antidomain(X1)))),inference(spm,[status(thm)],[1090,1530,theory(equality)])).
% cnf(43251,plain,(antidomain(X1)=antidomain(antidomain(antidomain(X1)))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[43145,42320,theory(equality)]),101,theory(equality)])).
% cnf(43288,plain,(multiplication(antidomain(X1),antidomain(antidomain(X1)))=multiplication(antidomain(antidomain(X1)),coantidomain(antidomain(antidomain(X1))))),inference(spm,[status(thm)],[1530,43251,theory(equality)])).
% cnf(43424,negated_conjecture,(addition(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))),antidomain(antidomain(esk3_0)))=antidomain(antidomain(esk3_0))),inference(rw,[status(thm)],[97,43251,theory(equality)])).
% cnf(43765,plain,(addition(zero,multiplication(X1,antidomain(antidomain(antidomain(coantidomain(X1))))))=X1),inference(spm,[status(thm)],[1090,42442,theory(equality)])).
% cnf(43940,plain,(multiplication(X1,antidomain(coantidomain(X1)))=X1),inference(rw,[status(thm)],[inference(rw,[status(thm)],[43765,43251,theory(equality)]),203,theory(equality)])).
% cnf(48660,plain,(addition(multiplication(X1,coantidomain(X1)),multiplication(coantidomain(coantidomain(X1)),antidomain(antidomain(antidomain(coantidomain(X1))))))=coantidomain(coantidomain(X1))),inference(spm,[status(thm)],[1090,42438,theory(equality)])).
% cnf(48753,plain,(multiplication(coantidomain(coantidomain(X1)),antidomain(coantidomain(X1)))=coantidomain(coantidomain(X1))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[48660,43251,theory(equality)]),234,theory(equality)])).
% cnf(50103,plain,(multiplication(antidomain(antidomain(antidomain(antidomain(X1)))),multiplication(antidomain(X1),antidomain(antidomain(X1))))=multiplication(antidomain(X1),antidomain(antidomain(X1)))),inference(spm,[status(thm)],[42319,43288,theory(equality)])).
% cnf(50206,plain,(multiplication(antidomain(X1),coantidomain(antidomain(X1)))=multiplication(antidomain(X1),antidomain(antidomain(X1)))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[50103,43251,theory(equality)]),1601,theory(equality)])).
% cnf(50294,plain,(addition(coantidomain(multiplication(antidomain(X1),coantidomain(antidomain(X1)))),coantidomain(multiplication(coantidomain(coantidomain(antidomain(X1))),antidomain(antidomain(X1)))))=coantidomain(multiplication(coantidomain(coantidomain(antidomain(X1))),antidomain(antidomain(X1))))),inference(spm,[status(thm)],[64,50206,theory(equality)])).
% cnf(50372,plain,(coantidomain(multiplication(antidomain(X1),coantidomain(antidomain(X1))))=coantidomain(multiplication(coantidomain(coantidomain(antidomain(X1))),antidomain(antidomain(X1))))),inference(rw,[status(thm)],[50294,1924,theory(equality)])).
% cnf(62197,plain,(antidomain(coantidomain(multiplication(multiplication(coantidomain(coantidomain(antidomain(X1))),antidomain(antidomain(X1))),coantidomain(multiplication(antidomain(X1),coantidomain(antidomain(X1)))))))=multiplication(multiplication(coantidomain(coantidomain(antidomain(X1))),antidomain(antidomain(X1))),coantidomain(multiplication(antidomain(X1),coantidomain(antidomain(X1)))))),inference(spm,[status(thm)],[445,50372,theory(equality)])).
% cnf(62396,plain,(multiplication(antidomain(X1),coantidomain(antidomain(X1)))=multiplication(multiplication(coantidomain(coantidomain(antidomain(X1))),antidomain(antidomain(X1))),coantidomain(multiplication(antidomain(X1),coantidomain(antidomain(X1)))))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[62197,38,theory(equality)]),463,theory(equality)]),50372,theory(equality)]),445,theory(equality)])).
% cnf(62397,plain,(multiplication(antidomain(X1),coantidomain(antidomain(X1)))=multiplication(coantidomain(coantidomain(antidomain(X1))),antidomain(antidomain(X1)))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[62396,38,theory(equality)]),463,theory(equality)])).
% cnf(62671,plain,(addition(multiplication(antidomain(X1),coantidomain(antidomain(X1))),multiplication(coantidomain(coantidomain(antidomain(X1))),antidomain(antidomain(antidomain(X1)))))=coantidomain(coantidomain(antidomain(X1)))),inference(spm,[status(thm)],[1090,62397,theory(equality)])).
% cnf(62764,plain,(multiplication(coantidomain(coantidomain(antidomain(X1))),antidomain(X1))=coantidomain(coantidomain(antidomain(X1)))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[62671,43251,theory(equality)]),234,theory(equality)])).
% cnf(70961,negated_conjecture,(leq(coantidomain(antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))))),antidomain(antidomain(esk3_0)))),inference(spm,[status(thm)],[42697,43424,theory(equality)])).
% cnf(71038,negated_conjecture,(leq(coantidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))),antidomain(antidomain(esk3_0)))),inference(rw,[status(thm)],[70961,43251,theory(equality)])).
% cnf(71063,negated_conjecture,(addition(coantidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))),antidomain(antidomain(esk3_0)))=antidomain(antidomain(esk3_0))),inference(spm,[status(thm)],[68,71038,theory(equality)])).
% cnf(84249,plain,(coantidomain(multiplication(X1,coantidomain(X1)))=antidomain(multiplication(X1,antidomain(antidomain(multiplication(coantidomain(X1),X2)))))),inference(rw,[status(thm)],[1392,1218,theory(equality)])).
% cnf(84317,plain,(multiplication(antidomain(coantidomain(multiplication(X1,coantidomain(X1)))),multiplication(X1,antidomain(antidomain(multiplication(coantidomain(X1),X2)))))=multiplication(X1,antidomain(antidomain(multiplication(coantidomain(X1),X2))))),inference(spm,[status(thm)],[42320,84249,theory(equality)])).
% cnf(84559,plain,(multiplication(X1,coantidomain(X1))=multiplication(X1,antidomain(antidomain(multiplication(coantidomain(X1),X2))))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[84317,445,theory(equality)]),38,theory(equality)]),1364,theory(equality)])).
% cnf(84990,plain,(addition(multiplication(antidomain(X1),X1),multiplication(antidomain(X1),multiplication(coantidomain(X2),X1)))=addition(multiplication(X1,coantidomain(X1)),multiplication(multiplication(coantidomain(X2),X1),coantidomain(X1)))),inference(spm,[status(thm)],[1609,2814,theory(equality)])).
% cnf(84993,plain,(addition(multiplication(antidomain(X1),X1),multiplication(antidomain(X1),multiplication(X1,coantidomain(X2))))=addition(multiplication(X1,coantidomain(X1)),multiplication(multiplication(X1,coantidomain(X2)),coantidomain(X1)))),inference(spm,[status(thm)],[1609,2975,theory(equality)])).
% cnf(85471,plain,(multiplication(antidomain(X1),multiplication(coantidomain(X2),X1))=addition(multiplication(X1,coantidomain(X1)),multiplication(multiplication(coantidomain(X2),X1),coantidomain(X1)))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[84990,1530,theory(equality)]),234,theory(equality)])).
% cnf(85472,plain,(multiplication(antidomain(X1),multiplication(coantidomain(X2),X1))=multiplication(X1,coantidomain(X1))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[85471,38,theory(equality)]),98,theory(equality)]),234,theory(equality)])).
% cnf(85477,plain,(multiplication(X1,coantidomain(X1))=addition(multiplication(X1,coantidomain(X1)),multiplication(multiplication(X1,coantidomain(X2)),coantidomain(X1)))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[84993,1530,theory(equality)]),1601,theory(equality)]),234,theory(equality)])).
% cnf(85478,plain,(multiplication(X1,coantidomain(X1))=multiplication(X1,multiplication(coantidomain(X2),coantidomain(X1)))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[85477,38,theory(equality)]),234,theory(equality)])).
% cnf(92244,plain,(addition(multiplication(antidomain(X1),multiplication(coantidomain(X2),antidomain(X1))),multiplication(antidomain(X1),coantidomain(antidomain(X1))))=multiplication(coantidomain(X2),antidomain(X1))),inference(spm,[status(thm)],[1089,85472,theory(equality)])).
% cnf(92249,plain,(addition(multiplication(X1,coantidomain(X1)),multiplication(antidomain(antidomain(X1)),multiplication(coantidomain(X2),X1)))=multiplication(coantidomain(X2),X1)),inference(spm,[status(thm)],[1089,85472,theory(equality)])).
% cnf(92257,plain,(multiplication(antidomain(coantidomain(X1)),coantidomain(antidomain(coantidomain(X1))))=multiplication(coantidomain(X1),antidomain(coantidomain(X1)))),inference(spm,[status(thm)],[42319,85472,theory(equality)])).
% cnf(92383,plain,(multiplication(antidomain(X1),multiplication(coantidomain(X2),antidomain(X1)))=multiplication(coantidomain(X2),antidomain(X1))),inference(rw,[status(thm)],[92244,101,theory(equality)])).
% cnf(92389,plain,(multiplication(antidomain(antidomain(X1)),multiplication(coantidomain(X2),X1))=multiplication(coantidomain(X2),X1)),inference(rw,[status(thm)],[92249,234,theory(equality)])).
% cnf(95541,plain,(multiplication(antidomain(antidomain(antidomain(coantidomain(X1)))),multiplication(coantidomain(X1),antidomain(coantidomain(X1))))=multiplication(coantidomain(X1),antidomain(coantidomain(X1)))),inference(spm,[status(thm)],[42319,92257,theory(equality)])).
% cnf(95668,plain,(multiplication(X1,coantidomain(X1))=multiplication(coantidomain(X1),antidomain(coantidomain(X1)))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[95541,43251,theory(equality)]),1601,theory(equality)]),1373,theory(equality)])).
% cnf(101206,plain,(addition(multiplication(X1,coantidomain(X1)),multiplication(X1,antidomain(antidomain(antidomain(multiplication(coantidomain(X1),X2))))))=X1),inference(spm,[status(thm)],[1090,84559,theory(equality)])).
% cnf(101404,plain,(multiplication(X1,antidomain(multiplication(coantidomain(X1),X2)))=X1),inference(rw,[status(thm)],[inference(rw,[status(thm)],[101206,43251,theory(equality)]),234,theory(equality)])).
% cnf(101569,plain,(leq(antidomain(X1),antidomain(multiplication(coantidomain(antidomain(X1)),X2)))),inference(spm,[status(thm)],[2103,101404,theory(equality)])).
% cnf(103349,plain,(multiplication(coantidomain(antidomain(X1)),antidomain(X1))=multiplication(antidomain(X1),coantidomain(antidomain(X1)))),inference(spm,[status(thm)],[1364,92383,theory(equality)])).
% cnf(103638,plain,(addition(multiplication(antidomain(X1),coantidomain(antidomain(X1))),multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1))))=coantidomain(antidomain(X1))),inference(spm,[status(thm)],[1090,103349,theory(equality)])).
% cnf(103779,plain,(multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1)))=coantidomain(antidomain(X1))),inference(rw,[status(thm)],[103638,234,theory(equality)])).
% cnf(106156,plain,(addition(multiplication(coantidomain(X1),antidomain(coantidomain(X1))),coantidomain(coantidomain(X1)))=antidomain(coantidomain(X1))),inference(spm,[status(thm)],[1780,48753,theory(equality)])).
% cnf(106158,plain,(addition(multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1))),multiplication(antidomain(X1),coantidomain(antidomain(X1))))=antidomain(antidomain(X1))),inference(spm,[status(thm)],[1780,62397,theory(equality)])).
% cnf(106159,plain,(addition(multiplication(coantidomain(antidomain(X1)),antidomain(X1)),coantidomain(coantidomain(antidomain(X1))))=antidomain(X1)),inference(spm,[status(thm)],[1780,62764,theory(equality)])).
% cnf(106361,plain,(coantidomain(coantidomain(X1))=antidomain(coantidomain(X1))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[106156,95668,theory(equality)]),234,theory(equality)])).
% cnf(106363,plain,(coantidomain(antidomain(X1))=antidomain(antidomain(X1))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[106158,103779,theory(equality)]),2091,theory(equality)])).
% cnf(106364,plain,(coantidomain(coantidomain(antidomain(X1)))=antidomain(X1)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[106159,103349,theory(equality)]),234,theory(equality)])).
% cnf(106594,plain,(multiplication(X1,coantidomain(coantidomain(X1)))=X1),inference(rw,[status(thm)],[43940,106361,theory(equality)])).
% cnf(106966,plain,(multiplication(coantidomain(antidomain(X1)),X1)=X1),inference(rw,[status(thm)],[42320,106363,theory(equality)])).
% cnf(106967,plain,(multiplication(coantidomain(antidomain(X1)),multiplication(X1,X2))=multiplication(X1,X2)),inference(rw,[status(thm)],[42319,106363,theory(equality)])).
% cnf(106978,plain,(multiplication(coantidomain(antidomain(X1)),multiplication(coantidomain(X2),X1))=multiplication(coantidomain(X2),X1)),inference(rw,[status(thm)],[92389,106363,theory(equality)])).
% cnf(106991,negated_conjecture,(multiplication(antidomain(esk3_0),multiplication(esk1_0,coantidomain(antidomain(esk2_0))))!=zero),inference(rw,[status(thm)],[92,106363,theory(equality)])).
% cnf(106993,negated_conjecture,(addition(coantidomain(antidomain(multiplication(esk1_0,coantidomain(antidomain(esk2_0))))),coantidomain(antidomain(esk3_0)))=antidomain(antidomain(esk3_0))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[71063,106363,theory(equality)]),106363,theory(equality)])).
% cnf(106994,negated_conjecture,(addition(coantidomain(antidomain(multiplication(esk1_0,coantidomain(antidomain(esk2_0))))),coantidomain(antidomain(esk3_0)))=coantidomain(antidomain(esk3_0))),inference(rw,[status(thm)],[106993,106363,theory(equality)])).
% cnf(107208,plain,(multiplication(antidomain(X1),multiplication(antidomain(X2),antidomain(X1)))=multiplication(antidomain(X2),antidomain(X1))),inference(spm,[status(thm)],[92383,106364,theory(equality)])).
% cnf(108081,plain,(addition(coantidomain(X1),multiplication(coantidomain(coantidomain(X1)),coantidomain(coantidomain(coantidomain(X1)))))=coantidomain(coantidomain(coantidomain(X1)))),inference(spm,[status(thm)],[1780,106594,theory(equality)])).
% cnf(108187,plain,(coantidomain(X1)=coantidomain(coantidomain(coantidomain(X1)))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[108081,1373,theory(equality)]),1373,theory(equality)]),101,theory(equality)])).
% cnf(108459,plain,(addition(zero,multiplication(X1,coantidomain(coantidomain(addition(X1,X2)))))=X1),inference(spm,[status(thm)],[1781,29332,theory(equality)])).
% cnf(108582,plain,(multiplication(X1,coantidomain(coantidomain(addition(X1,X2))))=X1),inference(rw,[status(thm)],[108459,203,theory(equality)])).
% cnf(113488,plain,(multiplication(antidomain(X1),antidomain(multiplication(X1,X2)))=antidomain(X1)),inference(spm,[status(thm)],[101404,106967,theory(equality)])).
% cnf(113495,plain,(leq(antidomain(X1),antidomain(multiplication(X1,X2)))),inference(spm,[status(thm)],[101569,106967,theory(equality)])).
% cnf(113736,plain,(addition(antidomain(X1),antidomain(multiplication(X1,X2)))=antidomain(multiplication(X1,X2))),inference(spm,[status(thm)],[68,113495,theory(equality)])).
% cnf(115415,plain,(multiplication(multiplication(X1,coantidomain(X2)),coantidomain(coantidomain(X1)))=multiplication(X1,coantidomain(X2))),inference(spm,[status(thm)],[108582,1781,theory(equality)])).
% cnf(115578,plain,(multiplication(X1,multiplication(coantidomain(X2),coantidomain(coantidomain(X1))))=multiplication(X1,coantidomain(X2))),inference(rw,[status(thm)],[115415,38,theory(equality)])).
% cnf(119653,plain,(leq(antidomain(coantidomain(antidomain(X1))),antidomain(multiplication(coantidomain(X2),X1)))),inference(spm,[status(thm)],[113495,106978,theory(equality)])).
% cnf(119685,plain,(multiplication(coantidomain(antidomain(X1)),multiplication(antidomain(X2),X1))=multiplication(antidomain(X2),X1)),inference(spm,[status(thm)],[106978,106364,theory(equality)])).
% cnf(119738,plain,(multiplication(coantidomain(coantidomain(coantidomain(X1))),multiplication(coantidomain(X2),coantidomain(X1)))=multiplication(coantidomain(X2),coantidomain(X1))),inference(spm,[status(thm)],[106978,106361,theory(equality)])).
% cnf(119781,plain,(leq(antidomain(X1),antidomain(multiplication(coantidomain(X2),X1)))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[119653,106361,theory(equality)]),106364,theory(equality)])).
% cnf(119883,plain,(multiplication(coantidomain(X1),multiplication(coantidomain(X2),coantidomain(X1)))=multiplication(coantidomain(X2),coantidomain(X1))),inference(rw,[status(thm)],[119738,108187,theory(equality)])).
% cnf(120207,plain,(leq(antidomain(coantidomain(coantidomain(addition(coantidomain(X1),X2)))),antidomain(coantidomain(X1)))),inference(spm,[status(thm)],[119781,108582,theory(equality)])).
% cnf(120281,plain,(leq(coantidomain(addition(coantidomain(X1),X2)),coantidomain(coantidomain(X1)))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[120207,106361,theory(equality)]),108187,theory(equality)]),106361,theory(equality)])).
% cnf(121661,negated_conjecture,(leq(coantidomain(coantidomain(antidomain(esk3_0))),coantidomain(coantidomain(antidomain(multiplication(esk1_0,coantidomain(antidomain(esk2_0)))))))),inference(spm,[status(thm)],[120281,106994,theory(equality)])).
% cnf(121721,negated_conjecture,(leq(antidomain(esk3_0),antidomain(multiplication(esk1_0,coantidomain(antidomain(esk2_0)))))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[121661,106364,theory(equality)]),106364,theory(equality)])).
% cnf(121724,negated_conjecture,(addition(antidomain(esk3_0),antidomain(multiplication(esk1_0,coantidomain(antidomain(esk2_0)))))=antidomain(multiplication(esk1_0,coantidomain(antidomain(esk2_0))))),inference(spm,[status(thm)],[68,121721,theory(equality)])).
% cnf(121725,negated_conjecture,(addition(antidomain(multiplication(esk1_0,coantidomain(antidomain(esk2_0)))),antidomain(esk3_0))=antidomain(multiplication(esk1_0,coantidomain(antidomain(esk2_0))))),inference(rw,[status(thm)],[121724,30,theory(equality)])).
% cnf(121764,negated_conjecture,(leq(antidomain(esk3_0),addition(antidomain(multiplication(esk1_0,coantidomain(antidomain(esk2_0)))),X1))|addition(X1,antidomain(multiplication(esk1_0,coantidomain(antidomain(esk2_0)))))!=addition(antidomain(multiplication(esk1_0,coantidomain(antidomain(esk2_0)))),X1)),inference(spm,[status(thm)],[5949,121725,theory(equality)])).
% cnf(121879,negated_conjecture,(leq(antidomain(esk3_0),addition(antidomain(multiplication(esk1_0,coantidomain(antidomain(esk2_0)))),X1))),inference(ar,[status(thm)],[121764,30,32,38,theory(equality)])).
% cnf(123072,plain,(multiplication(antidomain(multiplication(X1,X2)),antidomain(X1))=antidomain(X1)),inference(spm,[status(thm)],[107208,113488,theory(equality)])).
% cnf(123808,plain,(multiplication(coantidomain(X1),multiplication(coantidomain(X2),coantidomain(X1)))=multiplication(coantidomain(X1),coantidomain(X2))),inference(spm,[status(thm)],[115578,108187,theory(equality)])).
% cnf(126052,negated_conjecture,(leq(antidomain(esk3_0),antidomain(multiplication(multiplication(esk1_0,coantidomain(antidomain(esk2_0))),X1)))),inference(spm,[status(thm)],[121879,113736,theory(equality)])).
% cnf(126079,negated_conjecture,(leq(antidomain(esk3_0),antidomain(multiplication(esk1_0,multiplication(coantidomain(antidomain(esk2_0)),X1))))),inference(rw,[status(thm)],[126052,38,theory(equality)])).
% cnf(127729,plain,(multiplication(coantidomain(X2),coantidomain(X1))=multiplication(coantidomain(X1),coantidomain(X2))),inference(rw,[status(thm)],[123808,119883,theory(equality)])).
% cnf(128321,negated_conjecture,(leq(antidomain(esk3_0),antidomain(multiplication(esk1_0,esk2_0)))),inference(spm,[status(thm)],[126079,106966,theory(equality)])).
% cnf(128364,negated_conjecture,(addition(antidomain(esk3_0),antidomain(multiplication(esk1_0,esk2_0)))=antidomain(multiplication(esk1_0,esk2_0))),inference(spm,[status(thm)],[68,128321,theory(equality)])).
% cnf(128365,negated_conjecture,(addition(antidomain(multiplication(esk1_0,esk2_0)),antidomain(esk3_0))=antidomain(multiplication(esk1_0,esk2_0))),inference(rw,[status(thm)],[128364,30,theory(equality)])).
% cnf(128374,negated_conjecture,(addition(multiplication(antidomain(antidomain(multiplication(esk1_0,esk2_0))),antidomain(multiplication(esk1_0,esk2_0))),multiplication(antidomain(antidomain(multiplication(esk1_0,esk2_0))),antidomain(esk3_0)))=addition(multiplication(antidomain(multiplication(esk1_0,esk2_0)),coantidomain(antidomain(multiplication(esk1_0,esk2_0)))),multiplication(antidomain(esk3_0),coantidomain(antidomain(multiplication(esk1_0,esk2_0)))))),inference(spm,[status(thm)],[1609,128365,theory(equality)])).
% cnf(128381,negated_conjecture,(addition(multiplication(antidomain(multiplication(esk1_0,esk2_0)),coantidomain(antidomain(multiplication(esk1_0,esk2_0)))),multiplication(antidomain(esk3_0),coantidomain(antidomain(multiplication(esk1_0,esk2_0)))))=zero),inference(spm,[status(thm)],[979,128365,theory(equality)])).
% cnf(128493,negated_conjecture,(multiplication(coantidomain(antidomain(multiplication(esk1_0,esk2_0))),antidomain(esk3_0))=addition(multiplication(antidomain(multiplication(esk1_0,esk2_0)),coantidomain(antidomain(multiplication(esk1_0,esk2_0)))),multiplication(antidomain(esk3_0),coantidomain(antidomain(multiplication(esk1_0,esk2_0)))))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[128374,106363,theory(equality)]),103349,theory(equality)]),106363,theory(equality)]),234,theory(equality)])).
% cnf(128494,negated_conjecture,(multiplication(coantidomain(antidomain(multiplication(esk1_0,esk2_0))),antidomain(esk3_0))=multiplication(antidomain(esk3_0),coantidomain(antidomain(multiplication(esk1_0,esk2_0))))),inference(rw,[status(thm)],[128493,234,theory(equality)])).
% cnf(128504,negated_conjecture,(multiplication(antidomain(esk3_0),coantidomain(antidomain(multiplication(esk1_0,esk2_0))))=zero),inference(rw,[status(thm)],[128381,234,theory(equality)])).
% cnf(128882,negated_conjecture,(multiplication(coantidomain(antidomain(multiplication(esk1_0,esk2_0))),antidomain(esk3_0))=zero),inference(rw,[status(thm)],[128504,128494,theory(equality)])).
% cnf(128883,negated_conjecture,(multiplication(zero,X1)=multiplication(coantidomain(antidomain(multiplication(esk1_0,esk2_0))),multiplication(antidomain(esk3_0),X1))),inference(spm,[status(thm)],[38,128882,theory(equality)])).
% cnf(128945,negated_conjecture,(zero=multiplication(coantidomain(antidomain(multiplication(esk1_0,esk2_0))),multiplication(antidomain(esk3_0),X1))),inference(rw,[status(thm)],[128883,46,theory(equality)])).
% cnf(132122,negated_conjecture,(zero=multiplication(antidomain(esk3_0),multiplication(esk1_0,esk2_0))),inference(spm,[status(thm)],[119685,128945,theory(equality)])).
% cnf(132542,negated_conjecture,(addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(esk3_0),esk1_0))),esk2_0)))=coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(esk3_0),esk1_0))),esk2_0))),inference(spm,[status(thm)],[1651,132122,theory(equality)])).
% cnf(132607,negated_conjecture,(coantidomain(zero)=coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(esk3_0),esk1_0))),esk2_0))),inference(rw,[status(thm)],[132542,1860,theory(equality)])).
% cnf(132915,negated_conjecture,(multiplication(multiplication(coantidomain(coantidomain(multiplication(antidomain(esk3_0),esk1_0))),esk2_0),coantidomain(zero))=zero),inference(spm,[status(thm)],[62,132607,theory(equality)])).
% cnf(133103,negated_conjecture,(multiplication(coantidomain(coantidomain(multiplication(antidomain(esk3_0),esk1_0))),esk2_0)=zero),inference(rw,[status(thm)],[inference(rw,[status(thm)],[132915,38,theory(equality)]),435,theory(equality)])).
% cnf(133530,negated_conjecture,(addition(zero,multiplication(coantidomain(coantidomain(coantidomain(multiplication(antidomain(esk3_0),esk1_0)))),esk2_0))=esk2_0),inference(spm,[status(thm)],[1780,133103,theory(equality)])).
% cnf(133615,negated_conjecture,(multiplication(coantidomain(multiplication(antidomain(esk3_0),esk1_0)),esk2_0)=esk2_0),inference(rw,[status(thm)],[inference(rw,[status(thm)],[133530,108187,theory(equality)]),203,theory(equality)])).
% cnf(133678,negated_conjecture,(multiplication(antidomain(esk2_0),antidomain(coantidomain(multiplication(antidomain(esk3_0),esk1_0))))=antidomain(coantidomain(multiplication(antidomain(esk3_0),esk1_0)))),inference(spm,[status(thm)],[123072,133615,theory(equality)])).
% cnf(133736,negated_conjecture,(multiplication(antidomain(esk2_0),coantidomain(coantidomain(multiplication(antidomain(esk3_0),esk1_0))))=antidomain(coantidomain(multiplication(antidomain(esk3_0),esk1_0)))),inference(rw,[status(thm)],[133678,106361,theory(equality)])).
% cnf(133737,negated_conjecture,(multiplication(antidomain(esk2_0),coantidomain(coantidomain(multiplication(antidomain(esk3_0),esk1_0))))=coantidomain(coantidomain(multiplication(antidomain(esk3_0),esk1_0)))),inference(rw,[status(thm)],[133736,106361,theory(equality)])).
% cnf(133895,negated_conjecture,(multiplication(antidomain(coantidomain(coantidomain(multiplication(antidomain(esk3_0),esk1_0)))),antidomain(antidomain(esk2_0)))=antidomain(antidomain(esk2_0))),inference(spm,[status(thm)],[123072,133737,theory(equality)])).
% cnf(133958,negated_conjecture,(multiplication(coantidomain(multiplication(antidomain(esk3_0),esk1_0)),coantidomain(antidomain(esk2_0)))=antidomain(antidomain(esk2_0))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[133895,106361,theory(equality)]),108187,theory(equality)]),106363,theory(equality)])).
% cnf(133959,negated_conjecture,(multiplication(coantidomain(multiplication(antidomain(esk3_0),esk1_0)),coantidomain(antidomain(esk2_0)))=coantidomain(antidomain(esk2_0))),inference(rw,[status(thm)],[133958,106363,theory(equality)])).
% cnf(136670,negated_conjecture,(multiplication(coantidomain(antidomain(esk2_0)),coantidomain(multiplication(antidomain(esk3_0),esk1_0)))=coantidomain(antidomain(esk2_0))),inference(rw,[status(thm)],[133959,127729,theory(equality)])).
% cnf(136734,negated_conjecture,(multiplication(multiplication(antidomain(esk3_0),esk1_0),coantidomain(antidomain(esk2_0)))=multiplication(multiplication(antidomain(esk3_0),esk1_0),coantidomain(multiplication(antidomain(esk3_0),esk1_0)))),inference(spm,[status(thm)],[85478,136670,theory(equality)])).
% cnf(136809,negated_conjecture,(multiplication(antidomain(esk3_0),multiplication(esk1_0,coantidomain(antidomain(esk2_0))))=multiplication(multiplication(antidomain(esk3_0),esk1_0),coantidomain(multiplication(antidomain(esk3_0),esk1_0)))),inference(rw,[status(thm)],[136734,38,theory(equality)])).
% cnf(136810,negated_conjecture,(multiplication(antidomain(esk3_0),multiplication(esk1_0,coantidomain(antidomain(esk2_0))))=zero),inference(rw,[status(thm)],[inference(rw,[status(thm)],[136809,38,theory(equality)]),151,theory(equality)])).
% cnf(136811,negated_conjecture,($false),inference(sr,[status(thm)],[136810,106991,theory(equality)])).
% cnf(136812,negated_conjecture,($false),136811,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses : 4624
% # ...of these trivial : 751
% # ...subsumed : 3159
% # ...remaining for further processing: 714
% # Other redundant clauses eliminated : 0
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed : 1
% # Backward-rewritten : 287
% # Generated clauses : 70682
% # ...of the previous two non-trivial : 37982
% # Contextual simplify-reflections : 0
% # Paramodulations : 70676
% # Factorizations : 0
% # Equation resolutions : 6
% # Current number of processed clauses: 426
% # Positive orientable unit clauses: 303
% # Positive unorientable unit clauses: 17
% # Negative unit clauses : 1
% # Non-unit-clauses : 105
% # Current number of unprocessed clauses: 16445
% # ...number of literals in the above : 24555
% # Clause-clause subsumption calls (NU) : 12308
% # Rec. Clause-clause subsumption calls : 12308
% # Unit Clause-clause subsumption calls : 316
% # Rewrite failures with RHS unbound : 185
% # Indexed BW rewrite attempts : 933
% # Indexed BW rewrite successes : 300
% # Backwards rewriting index: 350 leaves, 1.81+/-1.499 terms/leaf
% # Paramod-from index: 225 leaves, 1.45+/-0.853 terms/leaf
% # Paramod-into index: 313 leaves, 1.78+/-1.515 terms/leaf
% # -------------------------------------------------
% # User time : 1.670 s
% # System time : 0.069 s
% # Total time : 1.739 s
% # Maximum resident set size: 0 pages
% PrfWatch: 3.37 CPU 3.51 WC
% FINAL PrfWatch: 3.37 CPU 3.51 WC
% SZS output end Solution for /tmp/SystemOnTPTP5337/KLE099+1.tptp
%
%------------------------------------------------------------------------------