TSTP Solution File: ALG071+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : ALG071+1 : TPTP v5.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 03:46:55 EST 2010
% Result : Theorem 0.36s
% Output : CNFRefutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 61
% Number of leaves : 5
% Syntax : Number of formulae : 159 ( 11 unt; 0 def)
% Number of atoms : 513 ( 120 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 654 ( 300 ~; 291 |; 39 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 198 ( 0 sgn 66 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( sorti2(X1)
=> ! [X2] :
( sorti2(X2)
=> sorti2(op2(X1,X2)) ) ),
file('/tmp/tmpyUWc18/sel_ALG071+1.p_1',ax2) ).
fof(2,axiom,
! [X1] :
( sorti1(X1)
=> ? [X2] :
( sorti1(X2)
& op1(X2,op1(X2,X1)) != X1
& op1(X1,op1(X2,X1)) = X2 ) ),
file('/tmp/tmpyUWc18/sel_ALG071+1.p_1',ax3) ).
fof(3,conjecture,
( ( ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) )
& ! [X2] :
( sorti2(X2)
=> sorti1(j(X2)) ) )
=> ~ ( ! [X3] :
( sorti1(X3)
=> ! [X4] :
( sorti1(X4)
=> h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
& ! [X5] :
( sorti2(X5)
=> ! [X6] :
( sorti2(X6)
=> j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
& ! [X7] :
( sorti2(X7)
=> h(j(X7)) = X7 )
& ! [X8] :
( sorti1(X8)
=> j(h(X8)) = X8 ) ) ),
file('/tmp/tmpyUWc18/sel_ALG071+1.p_1',co1) ).
fof(4,axiom,
! [X1] :
( sorti1(X1)
=> ! [X2] :
( sorti1(X2)
=> sorti1(op1(X1,X2)) ) ),
file('/tmp/tmpyUWc18/sel_ALG071+1.p_1',ax1) ).
fof(5,axiom,
~ ! [X1] :
( sorti2(X1)
=> ? [X2] :
( sorti2(X2)
& op2(X2,op2(X2,X1)) != X1
& op2(X1,op2(X2,X1)) = X2 ) ),
file('/tmp/tmpyUWc18/sel_ALG071+1.p_1',ax4) ).
fof(6,negated_conjecture,
~ ( ( ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) )
& ! [X2] :
( sorti2(X2)
=> sorti1(j(X2)) ) )
=> ~ ( ! [X3] :
( sorti1(X3)
=> ! [X4] :
( sorti1(X4)
=> h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
& ! [X5] :
( sorti2(X5)
=> ! [X6] :
( sorti2(X6)
=> j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
& ! [X7] :
( sorti2(X7)
=> h(j(X7)) = X7 )
& ! [X8] :
( sorti1(X8)
=> j(h(X8)) = X8 ) ) ),
inference(assume_negation,[status(cth)],[3]) ).
fof(7,plain,
! [X1] :
( ~ sorti2(X1)
| ! [X2] :
( ~ sorti2(X2)
| sorti2(op2(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(8,plain,
! [X3] :
( ~ sorti2(X3)
| ! [X4] :
( ~ sorti2(X4)
| sorti2(op2(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[7]) ).
fof(9,plain,
! [X3,X4] :
( ~ sorti2(X4)
| sorti2(op2(X3,X4))
| ~ sorti2(X3) ),
inference(shift_quantors,[status(thm)],[8]) ).
cnf(10,plain,
( sorti2(op2(X1,X2))
| ~ sorti2(X1)
| ~ sorti2(X2) ),
inference(split_conjunct,[status(thm)],[9]) ).
fof(11,plain,
! [X1] :
( ~ sorti1(X1)
| ? [X2] :
( sorti1(X2)
& op1(X2,op1(X2,X1)) != X1
& op1(X1,op1(X2,X1)) = X2 ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(12,plain,
! [X3] :
( ~ sorti1(X3)
| ? [X4] :
( sorti1(X4)
& op1(X4,op1(X4,X3)) != X3
& op1(X3,op1(X4,X3)) = X4 ) ),
inference(variable_rename,[status(thm)],[11]) ).
fof(13,plain,
! [X3] :
( ~ sorti1(X3)
| ( sorti1(esk1_1(X3))
& op1(esk1_1(X3),op1(esk1_1(X3),X3)) != X3
& op1(X3,op1(esk1_1(X3),X3)) = esk1_1(X3) ) ),
inference(skolemize,[status(esa)],[12]) ).
fof(14,plain,
! [X3] :
( ( sorti1(esk1_1(X3))
| ~ sorti1(X3) )
& ( op1(esk1_1(X3),op1(esk1_1(X3),X3)) != X3
| ~ sorti1(X3) )
& ( op1(X3,op1(esk1_1(X3),X3)) = esk1_1(X3)
| ~ sorti1(X3) ) ),
inference(distribute,[status(thm)],[13]) ).
cnf(15,plain,
( op1(X1,op1(esk1_1(X1),X1)) = esk1_1(X1)
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(16,plain,
( ~ sorti1(X1)
| op1(esk1_1(X1),op1(esk1_1(X1),X1)) != X1 ),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(17,plain,
( sorti1(esk1_1(X1))
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[14]) ).
fof(18,negated_conjecture,
( ! [X1] :
( ~ sorti1(X1)
| sorti2(h(X1)) )
& ! [X2] :
( ~ sorti2(X2)
| sorti1(j(X2)) )
& ! [X3] :
( ~ sorti1(X3)
| ! [X4] :
( ~ sorti1(X4)
| h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
& ! [X5] :
( ~ sorti2(X5)
| ! [X6] :
( ~ sorti2(X6)
| j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
& ! [X7] :
( ~ sorti2(X7)
| h(j(X7)) = X7 )
& ! [X8] :
( ~ sorti1(X8)
| j(h(X8)) = X8 ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(19,negated_conjecture,
( ! [X9] :
( ~ sorti1(X9)
| sorti2(h(X9)) )
& ! [X10] :
( ~ sorti2(X10)
| sorti1(j(X10)) )
& ! [X11] :
( ~ sorti1(X11)
| ! [X12] :
( ~ sorti1(X12)
| h(op1(X11,X12)) = op2(h(X11),h(X12)) ) )
& ! [X13] :
( ~ sorti2(X13)
| ! [X14] :
( ~ sorti2(X14)
| j(op2(X13,X14)) = op1(j(X13),j(X14)) ) )
& ! [X15] :
( ~ sorti2(X15)
| h(j(X15)) = X15 )
& ! [X16] :
( ~ sorti1(X16)
| j(h(X16)) = X16 ) ),
inference(variable_rename,[status(thm)],[18]) ).
fof(20,negated_conjecture,
! [X9,X10,X11,X12,X13,X14,X15,X16] :
( ( ~ sorti1(X16)
| j(h(X16)) = X16 )
& ( ~ sorti2(X15)
| h(j(X15)) = X15 )
& ( ~ sorti2(X14)
| j(op2(X13,X14)) = op1(j(X13),j(X14))
| ~ sorti2(X13) )
& ( ~ sorti1(X12)
| h(op1(X11,X12)) = op2(h(X11),h(X12))
| ~ sorti1(X11) )
& ( ~ sorti2(X10)
| sorti1(j(X10)) )
& ( ~ sorti1(X9)
| sorti2(h(X9)) ) ),
inference(shift_quantors,[status(thm)],[19]) ).
cnf(21,negated_conjecture,
( sorti2(h(X1))
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[20]) ).
cnf(22,negated_conjecture,
( sorti1(j(X1))
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[20]) ).
cnf(23,negated_conjecture,
( h(op1(X1,X2)) = op2(h(X1),h(X2))
| ~ sorti1(X1)
| ~ sorti1(X2) ),
inference(split_conjunct,[status(thm)],[20]) ).
cnf(24,negated_conjecture,
( j(op2(X1,X2)) = op1(j(X1),j(X2))
| ~ sorti2(X1)
| ~ sorti2(X2) ),
inference(split_conjunct,[status(thm)],[20]) ).
cnf(25,negated_conjecture,
( h(j(X1)) = X1
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[20]) ).
cnf(26,negated_conjecture,
( j(h(X1)) = X1
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[20]) ).
fof(27,plain,
! [X1] :
( ~ sorti1(X1)
| ! [X2] :
( ~ sorti1(X2)
| sorti1(op1(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(28,plain,
! [X3] :
( ~ sorti1(X3)
| ! [X4] :
( ~ sorti1(X4)
| sorti1(op1(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[27]) ).
fof(29,plain,
! [X3,X4] :
( ~ sorti1(X4)
| sorti1(op1(X3,X4))
| ~ sorti1(X3) ),
inference(shift_quantors,[status(thm)],[28]) ).
cnf(30,plain,
( sorti1(op1(X1,X2))
| ~ sorti1(X1)
| ~ sorti1(X2) ),
inference(split_conjunct,[status(thm)],[29]) ).
fof(31,plain,
? [X1] :
( sorti2(X1)
& ! [X2] :
( ~ sorti2(X2)
| op2(X2,op2(X2,X1)) = X1
| op2(X1,op2(X2,X1)) != X2 ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(32,plain,
? [X3] :
( sorti2(X3)
& ! [X4] :
( ~ sorti2(X4)
| op2(X4,op2(X4,X3)) = X3
| op2(X3,op2(X4,X3)) != X4 ) ),
inference(variable_rename,[status(thm)],[31]) ).
fof(33,plain,
( sorti2(esk2_0)
& ! [X4] :
( ~ sorti2(X4)
| op2(X4,op2(X4,esk2_0)) = esk2_0
| op2(esk2_0,op2(X4,esk2_0)) != X4 ) ),
inference(skolemize,[status(esa)],[32]) ).
fof(34,plain,
! [X4] :
( ( ~ sorti2(X4)
| op2(X4,op2(X4,esk2_0)) = esk2_0
| op2(esk2_0,op2(X4,esk2_0)) != X4 )
& sorti2(esk2_0) ),
inference(shift_quantors,[status(thm)],[33]) ).
cnf(35,plain,
sorti2(esk2_0),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(36,plain,
( op2(X1,op2(X1,esk2_0)) = esk2_0
| op2(esk2_0,op2(X1,esk2_0)) != X1
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(40,negated_conjecture,
( sorti2(op2(h(X1),h(X2)))
| ~ sorti1(op1(X1,X2))
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[21,23,theory(equality)]) ).
cnf(41,negated_conjecture,
( j(op2(h(X1),h(X2))) = op1(X1,X2)
| ~ sorti1(op1(X1,X2))
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[26,23,theory(equality)]) ).
cnf(42,negated_conjecture,
( h(esk1_1(X1)) = op2(h(X1),h(op1(esk1_1(X1),X1)))
| ~ sorti1(op1(esk1_1(X1),X1))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[23,15,theory(equality)]) ).
cnf(43,negated_conjecture,
( sorti1(op1(j(X1),j(X2)))
| ~ sorti2(op2(X1,X2))
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[22,24,theory(equality)]) ).
cnf(44,negated_conjecture,
( h(op1(j(X1),j(X2))) = op2(X1,X2)
| ~ sorti2(op2(X1,X2))
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[25,24,theory(equality)]) ).
cnf(46,negated_conjecture,
( sorti2(op2(h(X1),h(X2)))
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[40,30]) ).
cnf(48,negated_conjecture,
( sorti2(op2(h(X1),X2))
| ~ sorti1(j(X2))
| ~ sorti1(X1)
| ~ sorti2(X2) ),
inference(spm,[status(thm)],[46,25,theory(equality)]) ).
cnf(55,negated_conjecture,
( sorti2(op2(h(X1),X2))
| ~ sorti1(X1)
| ~ sorti2(X2) ),
inference(csr,[status(thm)],[48,22]) ).
cnf(57,negated_conjecture,
( sorti2(op2(op2(h(X1),h(X2)),X3))
| ~ sorti1(op1(X1,X2))
| ~ sorti2(X3)
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[55,23,theory(equality)]) ).
cnf(59,negated_conjecture,
( sorti1(op1(j(X1),j(X2)))
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[43,10]) ).
cnf(60,negated_conjecture,
( sorti1(op1(X1,j(X2)))
| ~ sorti2(X2)
| ~ sorti2(h(X1))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[59,26,theory(equality)]) ).
cnf(61,negated_conjecture,
( sorti1(op1(j(X1),X2))
| ~ sorti2(h(X2))
| ~ sorti2(X1)
| ~ sorti1(X2) ),
inference(spm,[status(thm)],[59,26,theory(equality)]) ).
cnf(64,negated_conjecture,
( sorti1(op1(X1,j(X2)))
| ~ sorti1(X1)
| ~ sorti2(X2) ),
inference(csr,[status(thm)],[60,21]) ).
cnf(68,negated_conjecture,
( sorti1(op1(j(X1),X2))
| ~ sorti1(X2)
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[61,21]) ).
cnf(70,negated_conjecture,
( sorti1(esk1_1(j(X1)))
| ~ sorti1(op1(esk1_1(j(X1)),j(X1)))
| ~ sorti2(X1)
| ~ sorti1(j(X1)) ),
inference(spm,[status(thm)],[68,15,theory(equality)]) ).
cnf(71,negated_conjecture,
( sorti1(op1(op1(j(X1),j(X2)),X3))
| ~ sorti1(X3)
| ~ sorti2(op2(X1,X2))
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[68,24,theory(equality)]) ).
cnf(73,negated_conjecture,
( j(op2(h(X1),h(X2))) = op1(X1,X2)
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[41,30]) ).
cnf(77,negated_conjecture,
( j(op2(h(X1),X2)) = op1(X1,j(X2))
| ~ sorti1(j(X2))
| ~ sorti1(X1)
| ~ sorti2(X2) ),
inference(spm,[status(thm)],[73,25,theory(equality)]) ).
cnf(85,negated_conjecture,
( op2(h(X1),h(op1(esk1_1(X1),X1))) = h(esk1_1(X1))
| ~ sorti1(X1)
| ~ sorti1(esk1_1(X1)) ),
inference(spm,[status(thm)],[42,30,theory(equality)]) ).
cnf(87,negated_conjecture,
( op2(h(X1),h(op1(esk1_1(X1),X1))) = h(esk1_1(X1))
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[85,17]) ).
cnf(91,negated_conjecture,
( op2(h(X1),op2(h(esk1_1(X1)),h(X1))) = h(esk1_1(X1))
| ~ sorti1(X1)
| ~ sorti1(esk1_1(X1)) ),
inference(spm,[status(thm)],[87,23,theory(equality)]) ).
cnf(97,negated_conjecture,
( op2(h(X1),op2(h(esk1_1(X1)),h(X1))) = h(esk1_1(X1))
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[91,17]) ).
cnf(98,negated_conjecture,
( op2(X1,op2(h(esk1_1(j(X1))),X1)) = h(esk1_1(j(X1)))
| ~ sorti1(j(X1))
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[97,25,theory(equality)]) ).
cnf(103,negated_conjecture,
( op2(X1,op2(h(esk1_1(j(X1))),X1)) = h(esk1_1(j(X1)))
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[98,22]) ).
cnf(108,negated_conjecture,
( op2(h(esk1_1(j(esk2_0))),op2(h(esk1_1(j(esk2_0))),esk2_0)) = esk2_0
| ~ sorti2(h(esk1_1(j(esk2_0))))
| ~ sorti2(esk2_0) ),
inference(spm,[status(thm)],[36,103,theory(equality)]) ).
cnf(111,negated_conjecture,
( op2(h(esk1_1(j(esk2_0))),op2(h(esk1_1(j(esk2_0))),esk2_0)) = esk2_0
| ~ sorti2(h(esk1_1(j(esk2_0))))
| $false ),
inference(rw,[status(thm)],[108,35,theory(equality)]) ).
cnf(112,negated_conjecture,
( op2(h(esk1_1(j(esk2_0))),op2(h(esk1_1(j(esk2_0))),esk2_0)) = esk2_0
| ~ sorti2(h(esk1_1(j(esk2_0)))) ),
inference(cn,[status(thm)],[111,theory(equality)]) ).
cnf(113,negated_conjecture,
( op2(h(esk1_1(j(esk2_0))),op2(h(esk1_1(j(esk2_0))),esk2_0)) = esk2_0
| ~ sorti1(esk1_1(j(esk2_0))) ),
inference(spm,[status(thm)],[112,21,theory(equality)]) ).
cnf(114,negated_conjecture,
( op2(h(esk1_1(j(esk2_0))),op2(h(esk1_1(j(esk2_0))),esk2_0)) = esk2_0
| ~ sorti1(j(esk2_0)) ),
inference(spm,[status(thm)],[113,17,theory(equality)]) ).
cnf(115,negated_conjecture,
( op2(h(esk1_1(j(esk2_0))),op2(h(esk1_1(j(esk2_0))),esk2_0)) = esk2_0
| ~ sorti2(esk2_0) ),
inference(spm,[status(thm)],[114,22,theory(equality)]) ).
cnf(116,negated_conjecture,
( op2(h(esk1_1(j(esk2_0))),op2(h(esk1_1(j(esk2_0))),esk2_0)) = esk2_0
| $false ),
inference(rw,[status(thm)],[115,35,theory(equality)]) ).
cnf(117,negated_conjecture,
op2(h(esk1_1(j(esk2_0))),op2(h(esk1_1(j(esk2_0))),esk2_0)) = esk2_0,
inference(cn,[status(thm)],[116,theory(equality)]) ).
cnf(148,negated_conjecture,
( sorti1(esk1_1(j(X1)))
| ~ sorti1(op1(esk1_1(j(X1)),j(X1)))
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[70,22]) ).
cnf(175,negated_conjecture,
( j(op2(h(X1),X2)) = op1(X1,j(X2))
| ~ sorti1(X1)
| ~ sorti2(X2) ),
inference(csr,[status(thm)],[77,22]) ).
cnf(176,negated_conjecture,
( j(esk2_0) = op1(esk1_1(j(esk2_0)),j(op2(h(esk1_1(j(esk2_0))),esk2_0)))
| ~ sorti1(esk1_1(j(esk2_0)))
| ~ sorti2(op2(h(esk1_1(j(esk2_0))),esk2_0)) ),
inference(spm,[status(thm)],[175,117,theory(equality)]) ).
cnf(186,negated_conjecture,
( op1(X1,j(h(X2))) = op1(X1,X2)
| ~ sorti1(X2)
| ~ sorti1(X1)
| ~ sorti2(h(X2)) ),
inference(spm,[status(thm)],[73,175,theory(equality)]) ).
cnf(205,negated_conjecture,
( h(op1(j(X1),j(X2))) = op2(X1,X2)
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[44,10]) ).
cnf(208,negated_conjecture,
( h(op1(X1,j(X2))) = op2(h(X1),X2)
| ~ sorti2(X2)
| ~ sorti2(h(X1))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[205,26,theory(equality)]) ).
cnf(232,negated_conjecture,
( op1(X1,j(h(X2))) = op1(X1,X2)
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[186,21]) ).
cnf(233,negated_conjecture,
( op1(esk1_1(j(h(X1))),op1(esk1_1(j(h(X1))),X1)) != j(h(X1))
| ~ sorti1(j(h(X1)))
| ~ sorti1(X1)
| ~ sorti1(esk1_1(j(h(X1)))) ),
inference(spm,[status(thm)],[16,232,theory(equality)]) ).
cnf(247,negated_conjecture,
( op1(esk1_1(j(h(X1))),op1(esk1_1(j(h(X1))),X1)) != j(h(X1))
| ~ sorti1(j(h(X1)))
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[233,17]) ).
cnf(248,negated_conjecture,
( op1(esk1_1(j(h(X1))),op1(esk1_1(j(h(X1))),X1)) != j(h(X1))
| ~ sorti1(X1)
| ~ sorti2(h(X1)) ),
inference(spm,[status(thm)],[247,22,theory(equality)]) ).
cnf(254,negated_conjecture,
( op1(esk1_1(j(h(X1))),op1(esk1_1(j(h(X1))),X1)) != j(h(X1))
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[248,21]) ).
cnf(257,negated_conjecture,
( op1(esk1_1(j(op2(h(X1),h(X2)))),op1(esk1_1(j(op2(h(X1),h(X2)))),op1(X1,X2))) != j(op2(h(X1),h(X2)))
| ~ sorti1(op1(X1,X2))
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[254,23,theory(equality)]) ).
cnf(281,negated_conjecture,
( h(op1(X1,j(X2))) = op2(h(X1),X2)
| ~ sorti1(X1)
| ~ sorti2(X2) ),
inference(csr,[status(thm)],[208,21]) ).
cnf(597,negated_conjecture,
( op1(esk1_1(j(op2(h(X1),h(X2)))),op1(esk1_1(j(op2(h(X1),h(X2)))),op1(X1,X2))) != j(op2(h(X1),h(X2)))
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[257,30]) ).
cnf(599,negated_conjecture,
( op1(esk1_1(j(op2(h(X1),X2))),op1(esk1_1(j(op2(h(X1),X2))),op1(X1,j(X2)))) != j(op2(h(X1),X2))
| ~ sorti1(j(X2))
| ~ sorti1(X1)
| ~ sorti2(X2) ),
inference(spm,[status(thm)],[597,25,theory(equality)]) ).
cnf(740,negated_conjecture,
( sorti2(op2(op2(h(X1),h(X2)),X3))
| ~ sorti1(X2)
| ~ sorti1(X1)
| ~ sorti2(X3) ),
inference(csr,[status(thm)],[57,30]) ).
cnf(745,negated_conjecture,
( sorti2(op2(h(esk1_1(X1)),X2))
| ~ sorti1(op1(esk1_1(X1),X1))
| ~ sorti1(X1)
| ~ sorti2(X2) ),
inference(spm,[status(thm)],[740,87,theory(equality)]) ).
cnf(1350,negated_conjecture,
( sorti1(op1(op1(j(X1),j(X2)),X3))
| ~ sorti1(X3)
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[71,10]) ).
cnf(1351,negated_conjecture,
( sorti1(op1(op1(X1,j(X2)),X3))
| ~ sorti1(X3)
| ~ sorti2(X2)
| ~ sorti2(h(X1))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[1350,26,theory(equality)]) ).
cnf(1436,negated_conjecture,
( sorti2(op2(h(esk1_1(X1)),X2))
| ~ sorti1(X1)
| ~ sorti2(X2)
| ~ sorti1(esk1_1(X1)) ),
inference(spm,[status(thm)],[745,30,theory(equality)]) ).
cnf(1440,negated_conjecture,
( sorti2(op2(h(esk1_1(X1)),X2))
| ~ sorti1(X1)
| ~ sorti2(X2) ),
inference(csr,[status(thm)],[1436,17]) ).
cnf(1721,negated_conjecture,
( op1(esk1_1(j(op2(h(X1),X2))),op1(esk1_1(j(op2(h(X1),X2))),op1(X1,j(X2)))) != j(op2(h(X1),X2))
| ~ sorti1(X1)
| ~ sorti2(X2) ),
inference(csr,[status(thm)],[599,22]) ).
cnf(1722,negated_conjecture,
( op1(esk1_1(j(esk2_0)),op1(esk1_1(j(esk2_0)),op1(esk1_1(j(esk2_0)),j(op2(h(esk1_1(j(esk2_0))),esk2_0))))) != j(esk2_0)
| ~ sorti1(esk1_1(j(esk2_0)))
| ~ sorti2(op2(h(esk1_1(j(esk2_0))),esk2_0)) ),
inference(spm,[status(thm)],[1721,117,theory(equality)]) ).
cnf(1774,negated_conjecture,
( sorti1(op1(op1(X1,j(X2)),X3))
| ~ sorti1(X1)
| ~ sorti1(X3)
| ~ sorti2(X2) ),
inference(csr,[status(thm)],[1351,21]) ).
cnf(1775,negated_conjecture,
( sorti1(op1(op1(X1,X2),X3))
| ~ sorti1(X3)
| ~ sorti1(X1)
| ~ sorti2(h(X2))
| ~ sorti1(X2) ),
inference(spm,[status(thm)],[1774,26,theory(equality)]) ).
cnf(1789,negated_conjecture,
( sorti1(op1(op1(X1,X2),X3))
| ~ sorti1(X2)
| ~ sorti1(X3)
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[1775,21]) ).
cnf(1790,negated_conjecture,
( sorti1(op1(esk1_1(X1),X2))
| ~ sorti1(X2)
| ~ sorti1(X1)
| ~ sorti1(op1(esk1_1(X1),X1)) ),
inference(spm,[status(thm)],[1789,15,theory(equality)]) ).
cnf(1798,negated_conjecture,
( sorti1(op1(esk1_1(X1),X2))
| ~ sorti1(X2)
| ~ sorti1(X1)
| ~ sorti1(esk1_1(X1)) ),
inference(spm,[status(thm)],[1790,30,theory(equality)]) ).
cnf(1806,negated_conjecture,
( sorti1(op1(esk1_1(X1),X2))
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[1798,17]) ).
cnf(1808,negated_conjecture,
( sorti1(esk1_1(j(X1)))
| ~ sorti2(X1)
| ~ sorti1(j(X1)) ),
inference(spm,[status(thm)],[148,1806,theory(equality)]) ).
cnf(1811,negated_conjecture,
( sorti1(esk1_1(j(X1)))
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[1808,22]) ).
cnf(1893,negated_conjecture,
( op1(esk1_1(j(esk2_0)),op1(esk1_1(j(esk2_0)),op1(esk1_1(j(esk2_0)),j(op2(h(esk1_1(j(esk2_0))),esk2_0))))) != j(esk2_0)
| ~ sorti2(op2(h(esk1_1(j(esk2_0))),esk2_0))
| ~ sorti2(esk2_0) ),
inference(spm,[status(thm)],[1722,1811,theory(equality)]) ).
cnf(1894,negated_conjecture,
( op1(esk1_1(j(esk2_0)),op1(esk1_1(j(esk2_0)),op1(esk1_1(j(esk2_0)),j(op2(h(esk1_1(j(esk2_0))),esk2_0))))) != j(esk2_0)
| ~ sorti2(op2(h(esk1_1(j(esk2_0))),esk2_0))
| $false ),
inference(rw,[status(thm)],[1893,35,theory(equality)]) ).
cnf(1895,negated_conjecture,
( op1(esk1_1(j(esk2_0)),op1(esk1_1(j(esk2_0)),op1(esk1_1(j(esk2_0)),j(op2(h(esk1_1(j(esk2_0))),esk2_0))))) != j(esk2_0)
| ~ sorti2(op2(h(esk1_1(j(esk2_0))),esk2_0)) ),
inference(cn,[status(thm)],[1894,theory(equality)]) ).
cnf(1902,negated_conjecture,
( op1(esk1_1(j(esk2_0)),op1(esk1_1(j(esk2_0)),op1(esk1_1(j(esk2_0)),j(op2(h(esk1_1(j(esk2_0))),esk2_0))))) != j(esk2_0)
| ~ sorti1(j(esk2_0))
| ~ sorti2(esk2_0) ),
inference(spm,[status(thm)],[1895,1440,theory(equality)]) ).
cnf(1907,negated_conjecture,
( op1(esk1_1(j(esk2_0)),op1(esk1_1(j(esk2_0)),op1(esk1_1(j(esk2_0)),j(op2(h(esk1_1(j(esk2_0))),esk2_0))))) != j(esk2_0)
| ~ sorti1(j(esk2_0))
| $false ),
inference(rw,[status(thm)],[1902,35,theory(equality)]) ).
cnf(1908,negated_conjecture,
( op1(esk1_1(j(esk2_0)),op1(esk1_1(j(esk2_0)),op1(esk1_1(j(esk2_0)),j(op2(h(esk1_1(j(esk2_0))),esk2_0))))) != j(esk2_0)
| ~ sorti1(j(esk2_0)) ),
inference(cn,[status(thm)],[1907,theory(equality)]) ).
cnf(1909,negated_conjecture,
( op1(esk1_1(j(esk2_0)),op1(esk1_1(j(esk2_0)),op1(esk1_1(j(esk2_0)),j(op2(h(esk1_1(j(esk2_0))),esk2_0))))) != j(esk2_0)
| ~ sorti2(esk2_0) ),
inference(spm,[status(thm)],[1908,22,theory(equality)]) ).
cnf(1910,negated_conjecture,
( op1(esk1_1(j(esk2_0)),op1(esk1_1(j(esk2_0)),op1(esk1_1(j(esk2_0)),j(op2(h(esk1_1(j(esk2_0))),esk2_0))))) != j(esk2_0)
| $false ),
inference(rw,[status(thm)],[1909,35,theory(equality)]) ).
cnf(1911,negated_conjecture,
op1(esk1_1(j(esk2_0)),op1(esk1_1(j(esk2_0)),op1(esk1_1(j(esk2_0)),j(op2(h(esk1_1(j(esk2_0))),esk2_0))))) != j(esk2_0),
inference(cn,[status(thm)],[1910,theory(equality)]) ).
cnf(2365,negated_conjecture,
( op1(esk1_1(j(esk2_0)),j(op2(h(esk1_1(j(esk2_0))),esk2_0))) = j(esk2_0)
| ~ sorti2(op2(h(esk1_1(j(esk2_0))),esk2_0))
| ~ sorti2(esk2_0) ),
inference(spm,[status(thm)],[176,1811,theory(equality)]) ).
cnf(2366,negated_conjecture,
( op1(esk1_1(j(esk2_0)),j(op2(h(esk1_1(j(esk2_0))),esk2_0))) = j(esk2_0)
| ~ sorti2(op2(h(esk1_1(j(esk2_0))),esk2_0))
| $false ),
inference(rw,[status(thm)],[2365,35,theory(equality)]) ).
cnf(2367,negated_conjecture,
( op1(esk1_1(j(esk2_0)),j(op2(h(esk1_1(j(esk2_0))),esk2_0))) = j(esk2_0)
| ~ sorti2(op2(h(esk1_1(j(esk2_0))),esk2_0)) ),
inference(cn,[status(thm)],[2366,theory(equality)]) ).
cnf(2371,negated_conjecture,
( op1(esk1_1(j(esk2_0)),j(op2(h(esk1_1(j(esk2_0))),esk2_0))) = j(esk2_0)
| ~ sorti1(j(esk2_0))
| ~ sorti2(esk2_0) ),
inference(spm,[status(thm)],[2367,1440,theory(equality)]) ).
cnf(2376,negated_conjecture,
( op1(esk1_1(j(esk2_0)),j(op2(h(esk1_1(j(esk2_0))),esk2_0))) = j(esk2_0)
| ~ sorti1(j(esk2_0))
| $false ),
inference(rw,[status(thm)],[2371,35,theory(equality)]) ).
cnf(2377,negated_conjecture,
( op1(esk1_1(j(esk2_0)),j(op2(h(esk1_1(j(esk2_0))),esk2_0))) = j(esk2_0)
| ~ sorti1(j(esk2_0)) ),
inference(cn,[status(thm)],[2376,theory(equality)]) ).
cnf(2486,negated_conjecture,
( op1(esk1_1(j(esk2_0)),j(op2(h(esk1_1(j(esk2_0))),esk2_0))) = j(esk2_0)
| ~ sorti2(esk2_0) ),
inference(spm,[status(thm)],[2377,22,theory(equality)]) ).
cnf(2487,negated_conjecture,
( op1(esk1_1(j(esk2_0)),j(op2(h(esk1_1(j(esk2_0))),esk2_0))) = j(esk2_0)
| $false ),
inference(rw,[status(thm)],[2486,35,theory(equality)]) ).
cnf(2488,negated_conjecture,
op1(esk1_1(j(esk2_0)),j(op2(h(esk1_1(j(esk2_0))),esk2_0))) = j(esk2_0),
inference(cn,[status(thm)],[2487,theory(equality)]) ).
cnf(2492,negated_conjecture,
( sorti1(j(esk2_0))
| ~ sorti1(esk1_1(j(esk2_0)))
| ~ sorti2(op2(h(esk1_1(j(esk2_0))),esk2_0)) ),
inference(spm,[status(thm)],[64,2488,theory(equality)]) ).
cnf(2494,negated_conjecture,
( h(j(esk2_0)) = op2(h(esk1_1(j(esk2_0))),op2(h(esk1_1(j(esk2_0))),esk2_0))
| ~ sorti1(esk1_1(j(esk2_0)))
| ~ sorti2(op2(h(esk1_1(j(esk2_0))),esk2_0)) ),
inference(spm,[status(thm)],[281,2488,theory(equality)]) ).
cnf(2519,negated_conjecture,
op1(esk1_1(j(esk2_0)),op1(esk1_1(j(esk2_0)),j(esk2_0))) != j(esk2_0),
inference(rw,[status(thm)],[1911,2488,theory(equality)]) ).
cnf(2530,negated_conjecture,
( h(j(esk2_0)) = esk2_0
| ~ sorti1(esk1_1(j(esk2_0)))
| ~ sorti2(op2(h(esk1_1(j(esk2_0))),esk2_0)) ),
inference(rw,[status(thm)],[2494,117,theory(equality)]) ).
cnf(2592,negated_conjecture,
( sorti1(j(esk2_0))
| ~ sorti2(op2(h(esk1_1(j(esk2_0))),esk2_0))
| ~ sorti2(esk2_0) ),
inference(spm,[status(thm)],[2492,1811,theory(equality)]) ).
cnf(2593,negated_conjecture,
( sorti1(j(esk2_0))
| ~ sorti2(op2(h(esk1_1(j(esk2_0))),esk2_0))
| $false ),
inference(rw,[status(thm)],[2592,35,theory(equality)]) ).
cnf(2594,negated_conjecture,
( sorti1(j(esk2_0))
| ~ sorti2(op2(h(esk1_1(j(esk2_0))),esk2_0)) ),
inference(cn,[status(thm)],[2593,theory(equality)]) ).
cnf(2596,negated_conjecture,
( sorti1(j(esk2_0))
| ~ sorti1(esk1_1(j(esk2_0)))
| ~ sorti2(esk2_0) ),
inference(spm,[status(thm)],[2594,55,theory(equality)]) ).
cnf(2601,negated_conjecture,
( sorti1(j(esk2_0))
| ~ sorti1(esk1_1(j(esk2_0)))
| $false ),
inference(rw,[status(thm)],[2596,35,theory(equality)]) ).
cnf(2602,negated_conjecture,
( sorti1(j(esk2_0))
| ~ sorti1(esk1_1(j(esk2_0))) ),
inference(cn,[status(thm)],[2601,theory(equality)]) ).
cnf(2606,negated_conjecture,
( sorti1(j(esk2_0))
| ~ sorti2(esk2_0) ),
inference(spm,[status(thm)],[2602,1811,theory(equality)]) ).
cnf(2607,negated_conjecture,
( sorti1(j(esk2_0))
| $false ),
inference(rw,[status(thm)],[2606,35,theory(equality)]) ).
cnf(2608,negated_conjecture,
sorti1(j(esk2_0)),
inference(cn,[status(thm)],[2607,theory(equality)]) ).
cnf(2634,negated_conjecture,
( h(j(esk2_0)) = esk2_0
| ~ sorti2(op2(h(esk1_1(j(esk2_0))),esk2_0))
| ~ sorti1(j(esk2_0)) ),
inference(spm,[status(thm)],[2530,17,theory(equality)]) ).
cnf(2636,negated_conjecture,
( h(j(esk2_0)) = esk2_0
| ~ sorti2(op2(h(esk1_1(j(esk2_0))),esk2_0))
| $false ),
inference(rw,[status(thm)],[2634,2608,theory(equality)]) ).
cnf(2637,negated_conjecture,
( h(j(esk2_0)) = esk2_0
| ~ sorti2(op2(h(esk1_1(j(esk2_0))),esk2_0)) ),
inference(cn,[status(thm)],[2636,theory(equality)]) ).
cnf(2643,negated_conjecture,
( h(j(esk2_0)) = esk2_0
| ~ sorti1(j(esk2_0))
| ~ sorti2(esk2_0) ),
inference(spm,[status(thm)],[2637,1440,theory(equality)]) ).
cnf(2648,negated_conjecture,
( h(j(esk2_0)) = esk2_0
| $false
| ~ sorti2(esk2_0) ),
inference(rw,[status(thm)],[2643,2608,theory(equality)]) ).
cnf(2649,negated_conjecture,
( h(j(esk2_0)) = esk2_0
| $false
| $false ),
inference(rw,[status(thm)],[2648,35,theory(equality)]) ).
cnf(2650,negated_conjecture,
h(j(esk2_0)) = esk2_0,
inference(cn,[status(thm)],[2649,theory(equality)]) ).
cnf(2652,negated_conjecture,
( sorti2(op2(esk2_0,h(X1)))
| ~ sorti1(X1)
| ~ sorti1(j(esk2_0)) ),
inference(spm,[status(thm)],[46,2650,theory(equality)]) ).
cnf(2656,negated_conjecture,
( j(op2(esk2_0,h(X1))) = op1(j(esk2_0),X1)
| ~ sorti1(X1)
| ~ sorti1(j(esk2_0)) ),
inference(spm,[status(thm)],[73,2650,theory(equality)]) ).
cnf(2657,negated_conjecture,
( j(op2(h(X1),esk2_0)) = op1(X1,j(esk2_0))
| ~ sorti1(j(esk2_0))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[73,2650,theory(equality)]) ).
cnf(2717,negated_conjecture,
( sorti2(op2(esk2_0,h(X1)))
| ~ sorti1(X1)
| $false ),
inference(rw,[status(thm)],[2652,2608,theory(equality)]) ).
cnf(2718,negated_conjecture,
( sorti2(op2(esk2_0,h(X1)))
| ~ sorti1(X1) ),
inference(cn,[status(thm)],[2717,theory(equality)]) ).
cnf(2725,negated_conjecture,
( j(op2(esk2_0,h(X1))) = op1(j(esk2_0),X1)
| ~ sorti1(X1)
| $false ),
inference(rw,[status(thm)],[2656,2608,theory(equality)]) ).
cnf(2726,negated_conjecture,
( j(op2(esk2_0,h(X1))) = op1(j(esk2_0),X1)
| ~ sorti1(X1) ),
inference(cn,[status(thm)],[2725,theory(equality)]) ).
cnf(2727,negated_conjecture,
( j(op2(h(X1),esk2_0)) = op1(X1,j(esk2_0))
| $false
| ~ sorti1(X1) ),
inference(rw,[status(thm)],[2657,2608,theory(equality)]) ).
cnf(2728,negated_conjecture,
( j(op2(h(X1),esk2_0)) = op1(X1,j(esk2_0))
| ~ sorti1(X1) ),
inference(cn,[status(thm)],[2727,theory(equality)]) ).
cnf(2965,negated_conjecture,
( sorti1(op1(j(esk2_0),X1))
| ~ sorti2(op2(esk2_0,h(X1)))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[22,2726,theory(equality)]) ).
cnf(3596,negated_conjecture,
( sorti1(op1(j(esk2_0),X1))
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[2965,2718]) ).
cnf(3597,negated_conjecture,
( sorti1(esk1_1(j(esk2_0)))
| ~ sorti1(op1(esk1_1(j(esk2_0)),j(esk2_0)))
| ~ sorti1(j(esk2_0)) ),
inference(spm,[status(thm)],[3596,15,theory(equality)]) ).
cnf(3600,negated_conjecture,
( sorti1(esk1_1(j(esk2_0)))
| ~ sorti1(op1(esk1_1(j(esk2_0)),j(esk2_0)))
| $false ),
inference(rw,[status(thm)],[3597,2608,theory(equality)]) ).
cnf(3601,negated_conjecture,
( sorti1(esk1_1(j(esk2_0)))
| ~ sorti1(op1(esk1_1(j(esk2_0)),j(esk2_0))) ),
inference(cn,[status(thm)],[3600,theory(equality)]) ).
cnf(3610,negated_conjecture,
( sorti1(esk1_1(j(esk2_0)))
| ~ sorti1(j(esk2_0)) ),
inference(spm,[status(thm)],[3601,1806,theory(equality)]) ).
cnf(3616,negated_conjecture,
( sorti1(esk1_1(j(esk2_0)))
| $false ),
inference(rw,[status(thm)],[3610,2608,theory(equality)]) ).
cnf(3617,negated_conjecture,
sorti1(esk1_1(j(esk2_0))),
inference(cn,[status(thm)],[3616,theory(equality)]) ).
cnf(4080,negated_conjecture,
( op1(esk1_1(j(esk2_0)),op1(esk1_1(j(esk2_0)),j(esk2_0))) = j(esk2_0)
| ~ sorti1(esk1_1(j(esk2_0))) ),
inference(spm,[status(thm)],[2488,2728,theory(equality)]) ).
cnf(4155,negated_conjecture,
( op1(esk1_1(j(esk2_0)),op1(esk1_1(j(esk2_0)),j(esk2_0))) = j(esk2_0)
| $false ),
inference(rw,[status(thm)],[4080,3617,theory(equality)]) ).
cnf(4156,negated_conjecture,
op1(esk1_1(j(esk2_0)),op1(esk1_1(j(esk2_0)),j(esk2_0))) = j(esk2_0),
inference(cn,[status(thm)],[4155,theory(equality)]) ).
cnf(4157,negated_conjecture,
$false,
inference(sr,[status(thm)],[4156,2519,theory(equality)]) ).
cnf(4158,negated_conjecture,
$false,
4157,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/ALG/ALG071+1.p
% --creating new selector for []
% -running prover on /tmp/tmpyUWc18/sel_ALG071+1.p_1 with time limit 29
% -prover status Theorem
% Problem ALG071+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/ALG/ALG071+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/ALG/ALG071+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
%
%------------------------------------------------------------------------------