TSTP Solution File: KLE090+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : KLE090+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %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 : Sat Dec 25 12:14:13 EST 2010
% Result : Theorem 1.89s
% Output : CNFRefutation 1.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 75 ( 70 unt; 0 def)
% Number of atoms : 80 ( 78 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 6 ~; 0 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 90 ( 2 sgn 42 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] : addition(X1,zero) = X1,
file('/tmp/tmp3lUOL_/sel_KLE090+1.p_1',additive_identity) ).
fof(3,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/tmp/tmp3lUOL_/sel_KLE090+1.p_1',left_distributivity) ).
fof(4,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/tmp/tmp3lUOL_/sel_KLE090+1.p_1',additive_associativity) ).
fof(5,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/tmp/tmp3lUOL_/sel_KLE090+1.p_1',additive_commutativity) ).
fof(6,axiom,
! [X1] : addition(X1,X1) = X1,
file('/tmp/tmp3lUOL_/sel_KLE090+1.p_1',additive_idempotence) ).
fof(12,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/tmp/tmp3lUOL_/sel_KLE090+1.p_1',multiplicative_right_identity) ).
fof(13,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/tmp/tmp3lUOL_/sel_KLE090+1.p_1',domain3) ).
fof(14,axiom,
! [X4,X5] : addition(antidomain(multiplication(X4,X5)),antidomain(multiplication(X4,antidomain(antidomain(X5))))) = antidomain(multiplication(X4,antidomain(antidomain(X5)))),
file('/tmp/tmp3lUOL_/sel_KLE090+1.p_1',domain2) ).
fof(15,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/tmp/tmp3lUOL_/sel_KLE090+1.p_1',right_distributivity) ).
fof(16,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/tmp/tmp3lUOL_/sel_KLE090+1.p_1',domain1) ).
fof(17,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/tmp/tmp3lUOL_/sel_KLE090+1.p_1',multiplicative_left_identity) ).
fof(18,conjecture,
! [X4,X5] :
( addition(X4,X5) = X5
=> addition(antidomain(X5),antidomain(X4)) = antidomain(X4) ),
file('/tmp/tmp3lUOL_/sel_KLE090+1.p_1',goals) ).
fof(19,negated_conjecture,
~ ! [X4,X5] :
( addition(X4,X5) = X5
=> addition(antidomain(X5),antidomain(X4)) = antidomain(X4) ),
inference(assume_negation,[status(cth)],[18]) ).
fof(22,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[2]) ).
cnf(23,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[22]) ).
fof(24,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[3]) ).
cnf(25,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[24]) ).
fof(26,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[4]) ).
cnf(27,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[26]) ).
fof(28,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[5]) ).
cnf(29,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[28]) ).
fof(30,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[6]) ).
cnf(31,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[30]) ).
fof(42,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[12]) ).
cnf(43,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[42]) ).
fof(44,plain,
! [X5] : addition(antidomain(antidomain(X5)),antidomain(X5)) = one,
inference(variable_rename,[status(thm)],[13]) ).
cnf(45,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[44]) ).
fof(46,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)],[14]) ).
cnf(47,plain,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
inference(split_conjunct,[status(thm)],[46]) ).
fof(48,plain,
! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
inference(variable_rename,[status(thm)],[15]) ).
cnf(49,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[48]) ).
fof(50,plain,
! [X5] : multiplication(antidomain(X5),X5) = zero,
inference(variable_rename,[status(thm)],[16]) ).
cnf(51,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[50]) ).
fof(52,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[17]) ).
cnf(53,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[52]) ).
fof(54,negated_conjecture,
? [X4,X5] :
( addition(X4,X5) = X5
& addition(antidomain(X5),antidomain(X4)) != antidomain(X4) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(55,negated_conjecture,
? [X6,X7] :
( addition(X6,X7) = X7
& addition(antidomain(X7),antidomain(X6)) != antidomain(X6) ),
inference(variable_rename,[status(thm)],[54]) ).
fof(56,negated_conjecture,
( addition(esk1_0,esk2_0) = esk2_0
& addition(antidomain(esk2_0),antidomain(esk1_0)) != antidomain(esk1_0) ),
inference(skolemize,[status(esa)],[55]) ).
cnf(57,negated_conjecture,
addition(antidomain(esk2_0),antidomain(esk1_0)) != antidomain(esk1_0),
inference(split_conjunct,[status(thm)],[56]) ).
cnf(58,negated_conjecture,
addition(esk1_0,esk2_0) = esk2_0,
inference(split_conjunct,[status(thm)],[56]) ).
cnf(60,plain,
zero = antidomain(one),
inference(spm,[status(thm)],[43,51,theory(equality)]) ).
cnf(63,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[23,29,theory(equality)]) ).
cnf(67,negated_conjecture,
addition(antidomain(esk1_0),antidomain(esk2_0)) != antidomain(esk1_0),
inference(rw,[status(thm)],[57,29,theory(equality)]) ).
cnf(68,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[45,29,theory(equality)]) ).
cnf(71,plain,
addition(X1,X2) = addition(X1,addition(X1,X2)),
inference(spm,[status(thm)],[27,31,theory(equality)]) ).
cnf(121,plain,
addition(multiplication(antidomain(X1),X2),zero) = multiplication(antidomain(X1),addition(X2,X1)),
inference(spm,[status(thm)],[49,51,theory(equality)]) ).
cnf(140,plain,
multiplication(antidomain(X1),X2) = multiplication(antidomain(X1),addition(X2,X1)),
inference(rw,[status(thm)],[121,23,theory(equality)]) ).
cnf(154,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(spm,[status(thm)],[25,53,theory(equality)]) ).
cnf(159,plain,
addition(multiplication(X1,X2),zero) = multiplication(addition(X1,antidomain(X2)),X2),
inference(spm,[status(thm)],[25,51,theory(equality)]) ).
cnf(179,plain,
multiplication(X1,X2) = multiplication(addition(X1,antidomain(X2)),X2),
inference(rw,[status(thm)],[159,23,theory(equality)]) ).
cnf(225,plain,
addition(zero,antidomain(zero)) = one,
inference(spm,[status(thm)],[68,60,theory(equality)]) ).
cnf(242,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[225,63,theory(equality)]) ).
cnf(302,plain,
addition(antidomain(X1),one) = one,
inference(spm,[status(thm)],[71,68,theory(equality)]) ).
cnf(320,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[302,29,theory(equality)]) ).
cnf(467,plain,
multiplication(addition(antidomain(X2),X1),X2) = multiplication(X1,X2),
inference(spm,[status(thm)],[179,29,theory(equality)]) ).
cnf(673,plain,
multiplication(one,X1) = multiplication(antidomain(antidomain(X1)),X1),
inference(spm,[status(thm)],[467,68,theory(equality)]) ).
cnf(695,plain,
X1 = multiplication(antidomain(antidomain(X1)),X1),
inference(rw,[status(thm)],[673,53,theory(equality)]) ).
cnf(2730,negated_conjecture,
multiplication(antidomain(esk2_0),esk2_0) = multiplication(antidomain(esk2_0),esk1_0),
inference(spm,[status(thm)],[140,58,theory(equality)]) ).
cnf(2731,plain,
multiplication(antidomain(antidomain(antidomain(X1))),one) = multiplication(antidomain(antidomain(antidomain(X1))),antidomain(X1)),
inference(spm,[status(thm)],[140,68,theory(equality)]) ).
cnf(2784,negated_conjecture,
zero = multiplication(antidomain(esk2_0),esk1_0),
inference(rw,[status(thm)],[2730,51,theory(equality)]) ).
cnf(2785,plain,
antidomain(antidomain(antidomain(X1))) = multiplication(antidomain(antidomain(antidomain(X1))),antidomain(X1)),
inference(rw,[status(thm)],[2731,43,theory(equality)]) ).
cnf(2786,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[2785,695,theory(equality)]) ).
cnf(2904,negated_conjecture,
addition(antidomain(zero),antidomain(multiplication(antidomain(esk2_0),antidomain(antidomain(esk1_0))))) = antidomain(multiplication(antidomain(esk2_0),antidomain(antidomain(esk1_0)))),
inference(spm,[status(thm)],[47,2784,theory(equality)]) ).
cnf(2914,negated_conjecture,
one = antidomain(multiplication(antidomain(esk2_0),antidomain(antidomain(esk1_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[2904,242,theory(equality)]),320,theory(equality)]) ).
cnf(3281,negated_conjecture,
multiplication(one,multiplication(antidomain(esk2_0),antidomain(antidomain(esk1_0)))) = zero,
inference(spm,[status(thm)],[51,2914,theory(equality)]) ).
cnf(3300,negated_conjecture,
multiplication(antidomain(esk2_0),antidomain(antidomain(esk1_0))) = zero,
inference(rw,[status(thm)],[3281,53,theory(equality)]) ).
cnf(3427,negated_conjecture,
addition(zero,multiplication(antidomain(esk2_0),X1)) = multiplication(antidomain(esk2_0),addition(antidomain(antidomain(esk1_0)),X1)),
inference(spm,[status(thm)],[49,3300,theory(equality)]) ).
cnf(3442,negated_conjecture,
multiplication(antidomain(esk2_0),X1) = multiplication(antidomain(esk2_0),addition(antidomain(antidomain(esk1_0)),X1)),
inference(rw,[status(thm)],[3427,63,theory(equality)]) ).
cnf(61052,negated_conjecture,
multiplication(antidomain(esk2_0),one) = multiplication(antidomain(esk2_0),antidomain(antidomain(antidomain(esk1_0)))),
inference(spm,[status(thm)],[3442,68,theory(equality)]) ).
cnf(61143,negated_conjecture,
antidomain(esk2_0) = multiplication(antidomain(esk2_0),antidomain(antidomain(antidomain(esk1_0)))),
inference(rw,[status(thm)],[61052,43,theory(equality)]) ).
cnf(61144,negated_conjecture,
antidomain(esk2_0) = multiplication(antidomain(esk2_0),antidomain(esk1_0)),
inference(rw,[status(thm)],[61143,2786,theory(equality)]) ).
cnf(61235,negated_conjecture,
addition(antidomain(esk1_0),antidomain(esk2_0)) = multiplication(addition(one,antidomain(esk2_0)),antidomain(esk1_0)),
inference(spm,[status(thm)],[154,61144,theory(equality)]) ).
cnf(61287,negated_conjecture,
addition(antidomain(esk1_0),antidomain(esk2_0)) = antidomain(esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[61235,320,theory(equality)]),53,theory(equality)]) ).
cnf(61288,negated_conjecture,
$false,
inference(sr,[status(thm)],[61287,67,theory(equality)]) ).
cnf(61289,negated_conjecture,
$false,
61288,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE090+1.p
% --creating new selector for [KLE001+0.ax, KLE001+4.ax]
% -running prover on /tmp/tmp3lUOL_/sel_KLE090+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE090+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE090+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE090+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
%
%------------------------------------------------------------------------------