TSTP Solution File: ALG072+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : ALG072+1 : TPTP v5.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 03:47:05 EST 2010
% Result : Theorem 4.54s
% Output : CNFRefutation 4.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 8
% Syntax : Number of formulae : 131 ( 21 unt; 0 def)
% Number of atoms : 458 ( 181 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 540 ( 213 ~; 216 |; 85 &)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 161 ( 0 sgn 78 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
( ! [X1] :
( sorti1(X1)
=> ( op1(unit1,X1) = X1
& op1(X1,unit1) = X1 ) )
& ? [X2] :
( sorti1(X2)
& unit1 = X2 ) ),
file('/tmp/tmpVtabsf/sel_ALG072+1.p_1',ax2) ).
fof(2,axiom,
sorti2(unit2),
file('/tmp/tmpVtabsf/sel_ALG072+1.p_1',ax3) ).
fof(3,axiom,
sorti1(unit1),
file('/tmp/tmpVtabsf/sel_ALG072+1.p_1',ax1) ).
fof(4,axiom,
! [X1] :
( sorti2(X1)
=> ! [X2] :
( sorti2(X2)
=> sorti2(op2(X1,X2)) ) ),
file('/tmp/tmpVtabsf/sel_ALG072+1.p_1',ax6) ).
fof(5,axiom,
? [X1] :
( sorti1(X1)
& ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> ( op1(X2,X3) != X1
| ( op1(X2,X1) = X3
& X1 != unit1 ) ) ) ) ),
file('/tmp/tmpVtabsf/sel_ALG072+1.p_1',ax7) ).
fof(6,axiom,
( ! [X1] :
( sorti2(X1)
=> ( op2(unit2,X1) = X1
& op2(X1,unit2) = X1 ) )
& ? [X2] :
( sorti2(X2)
& unit2 = X2 ) ),
file('/tmp/tmpVtabsf/sel_ALG072+1.p_1',ax4) ).
fof(8,axiom,
~ ? [X1] :
( sorti2(X1)
& ! [X2] :
( sorti2(X2)
=> ! [X3] :
( sorti2(X3)
=> ( op2(X2,X3) != X1
| ( op2(X2,X1) = X3
& X1 != unit2 ) ) ) ) ),
file('/tmp/tmpVtabsf/sel_ALG072+1.p_1',ax8) ).
fof(9,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/tmpVtabsf/sel_ALG072+1.p_1',co1) ).
fof(10,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)],[9]) ).
fof(11,plain,
( ! [X1] :
( ~ sorti1(X1)
| ( op1(unit1,X1) = X1
& op1(X1,unit1) = X1 ) )
& ? [X2] :
( sorti1(X2)
& unit1 = X2 ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(12,plain,
( ! [X3] :
( ~ sorti1(X3)
| ( op1(unit1,X3) = X3
& op1(X3,unit1) = X3 ) )
& ? [X4] :
( sorti1(X4)
& unit1 = X4 ) ),
inference(variable_rename,[status(thm)],[11]) ).
fof(13,plain,
( ! [X3] :
( ~ sorti1(X3)
| ( op1(unit1,X3) = X3
& op1(X3,unit1) = X3 ) )
& sorti1(esk1_0)
& unit1 = esk1_0 ),
inference(skolemize,[status(esa)],[12]) ).
fof(14,plain,
! [X3] :
( ( ~ sorti1(X3)
| ( op1(unit1,X3) = X3
& op1(X3,unit1) = X3 ) )
& sorti1(esk1_0)
& unit1 = esk1_0 ),
inference(shift_quantors,[status(thm)],[13]) ).
fof(15,plain,
! [X3] :
( ( op1(unit1,X3) = X3
| ~ sorti1(X3) )
& ( op1(X3,unit1) = X3
| ~ sorti1(X3) )
& sorti1(esk1_0)
& unit1 = esk1_0 ),
inference(distribute,[status(thm)],[14]) ).
cnf(19,plain,
( op1(unit1,X1) = X1
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[15]) ).
cnf(20,plain,
sorti2(unit2),
inference(split_conjunct,[status(thm)],[2]) ).
cnf(21,plain,
sorti1(unit1),
inference(split_conjunct,[status(thm)],[3]) ).
fof(22,plain,
! [X1] :
( ~ sorti2(X1)
| ! [X2] :
( ~ sorti2(X2)
| sorti2(op2(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(23,plain,
! [X3] :
( ~ sorti2(X3)
| ! [X4] :
( ~ sorti2(X4)
| sorti2(op2(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[22]) ).
fof(24,plain,
! [X3,X4] :
( ~ sorti2(X4)
| sorti2(op2(X3,X4))
| ~ sorti2(X3) ),
inference(shift_quantors,[status(thm)],[23]) ).
cnf(25,plain,
( sorti2(op2(X1,X2))
| ~ sorti2(X1)
| ~ sorti2(X2) ),
inference(split_conjunct,[status(thm)],[24]) ).
fof(26,plain,
? [X1] :
( sorti1(X1)
& ! [X2] :
( ~ sorti1(X2)
| ! [X3] :
( ~ sorti1(X3)
| op1(X2,X3) != X1
| ( op1(X2,X1) = X3
& X1 != unit1 ) ) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(27,plain,
? [X4] :
( sorti1(X4)
& ! [X5] :
( ~ sorti1(X5)
| ! [X6] :
( ~ sorti1(X6)
| op1(X5,X6) != X4
| ( op1(X5,X4) = X6
& X4 != unit1 ) ) ) ),
inference(variable_rename,[status(thm)],[26]) ).
fof(28,plain,
( sorti1(esk2_0)
& ! [X5] :
( ~ sorti1(X5)
| ! [X6] :
( ~ sorti1(X6)
| op1(X5,X6) != esk2_0
| ( op1(X5,esk2_0) = X6
& esk2_0 != unit1 ) ) ) ),
inference(skolemize,[status(esa)],[27]) ).
fof(29,plain,
! [X5,X6] :
( ( ~ sorti1(X6)
| op1(X5,X6) != esk2_0
| ( op1(X5,esk2_0) = X6
& esk2_0 != unit1 )
| ~ sorti1(X5) )
& sorti1(esk2_0) ),
inference(shift_quantors,[status(thm)],[28]) ).
fof(30,plain,
! [X5,X6] :
( ( op1(X5,esk2_0) = X6
| op1(X5,X6) != esk2_0
| ~ sorti1(X6)
| ~ sorti1(X5) )
& ( esk2_0 != unit1
| op1(X5,X6) != esk2_0
| ~ sorti1(X6)
| ~ sorti1(X5) )
& sorti1(esk2_0) ),
inference(distribute,[status(thm)],[29]) ).
cnf(31,plain,
sorti1(esk2_0),
inference(split_conjunct,[status(thm)],[30]) ).
cnf(32,plain,
( ~ sorti1(X1)
| ~ sorti1(X2)
| op1(X1,X2) != esk2_0
| esk2_0 != unit1 ),
inference(split_conjunct,[status(thm)],[30]) ).
cnf(33,plain,
( op1(X1,esk2_0) = X2
| ~ sorti1(X1)
| ~ sorti1(X2)
| op1(X1,X2) != esk2_0 ),
inference(split_conjunct,[status(thm)],[30]) ).
fof(34,plain,
( ! [X1] :
( ~ sorti2(X1)
| ( op2(unit2,X1) = X1
& op2(X1,unit2) = X1 ) )
& ? [X2] :
( sorti2(X2)
& unit2 = X2 ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(35,plain,
( ! [X3] :
( ~ sorti2(X3)
| ( op2(unit2,X3) = X3
& op2(X3,unit2) = X3 ) )
& ? [X4] :
( sorti2(X4)
& unit2 = X4 ) ),
inference(variable_rename,[status(thm)],[34]) ).
fof(36,plain,
( ! [X3] :
( ~ sorti2(X3)
| ( op2(unit2,X3) = X3
& op2(X3,unit2) = X3 ) )
& sorti2(esk3_0)
& unit2 = esk3_0 ),
inference(skolemize,[status(esa)],[35]) ).
fof(37,plain,
! [X3] :
( ( ~ sorti2(X3)
| ( op2(unit2,X3) = X3
& op2(X3,unit2) = X3 ) )
& sorti2(esk3_0)
& unit2 = esk3_0 ),
inference(shift_quantors,[status(thm)],[36]) ).
fof(38,plain,
! [X3] :
( ( op2(unit2,X3) = X3
| ~ sorti2(X3) )
& ( op2(X3,unit2) = X3
| ~ sorti2(X3) )
& sorti2(esk3_0)
& unit2 = esk3_0 ),
inference(distribute,[status(thm)],[37]) ).
cnf(41,plain,
( op2(X1,unit2) = X1
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[38]) ).
fof(47,plain,
! [X1] :
( ~ sorti2(X1)
| ? [X2] :
( sorti2(X2)
& ? [X3] :
( sorti2(X3)
& op2(X2,X3) = X1
& ( op2(X2,X1) != X3
| X1 = unit2 ) ) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(48,plain,
! [X4] :
( ~ sorti2(X4)
| ? [X5] :
( sorti2(X5)
& ? [X6] :
( sorti2(X6)
& op2(X5,X6) = X4
& ( op2(X5,X4) != X6
| X4 = unit2 ) ) ) ),
inference(variable_rename,[status(thm)],[47]) ).
fof(49,plain,
! [X4] :
( ~ sorti2(X4)
| ( sorti2(esk4_1(X4))
& sorti2(esk5_1(X4))
& op2(esk4_1(X4),esk5_1(X4)) = X4
& ( op2(esk4_1(X4),X4) != esk5_1(X4)
| X4 = unit2 ) ) ),
inference(skolemize,[status(esa)],[48]) ).
fof(50,plain,
! [X4] :
( ( sorti2(esk4_1(X4))
| ~ sorti2(X4) )
& ( sorti2(esk5_1(X4))
| ~ sorti2(X4) )
& ( op2(esk4_1(X4),esk5_1(X4)) = X4
| ~ sorti2(X4) )
& ( op2(esk4_1(X4),X4) != esk5_1(X4)
| X4 = unit2
| ~ sorti2(X4) ) ),
inference(distribute,[status(thm)],[49]) ).
cnf(51,plain,
( X1 = unit2
| ~ sorti2(X1)
| op2(esk4_1(X1),X1) != esk5_1(X1) ),
inference(split_conjunct,[status(thm)],[50]) ).
cnf(52,plain,
( op2(esk4_1(X1),esk5_1(X1)) = X1
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[50]) ).
cnf(53,plain,
( sorti2(esk5_1(X1))
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[50]) ).
cnf(54,plain,
( sorti2(esk4_1(X1))
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[50]) ).
fof(55,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)],[10]) ).
fof(56,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)],[55]) ).
fof(57,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)],[56]) ).
cnf(58,negated_conjecture,
( sorti2(h(X1))
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[57]) ).
cnf(59,negated_conjecture,
( sorti1(j(X1))
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[57]) ).
cnf(60,negated_conjecture,
( h(op1(X1,X2)) = op2(h(X1),h(X2))
| ~ sorti1(X1)
| ~ sorti1(X2) ),
inference(split_conjunct,[status(thm)],[57]) ).
cnf(61,negated_conjecture,
( j(op2(X1,X2)) = op1(j(X1),j(X2))
| ~ sorti2(X1)
| ~ sorti2(X2) ),
inference(split_conjunct,[status(thm)],[57]) ).
cnf(62,negated_conjecture,
( h(j(X1)) = X1
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[57]) ).
cnf(63,negated_conjecture,
( j(h(X1)) = X1
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[57]) ).
cnf(81,negated_conjecture,
( op1(X1,j(X2)) = j(op2(h(X1),X2))
| ~ sorti2(X2)
| ~ sorti2(h(X1))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[61,63,theory(equality)]) ).
cnf(82,negated_conjecture,
( op1(j(X1),X2) = j(op2(X1,h(X2)))
| ~ sorti2(h(X2))
| ~ sorti2(X1)
| ~ sorti1(X2) ),
inference(spm,[status(thm)],[61,63,theory(equality)]) ).
cnf(84,negated_conjecture,
( op2(X1,h(X2)) = h(op1(j(X1),X2))
| ~ sorti1(X2)
| ~ sorti1(j(X1))
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[60,62,theory(equality)]) ).
cnf(86,negated_conjecture,
( sorti2(h(op1(X1,X2)))
| ~ sorti2(h(X2))
| ~ sorti2(h(X1))
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[25,60,theory(equality)]) ).
cnf(88,plain,
( op1(unit1,esk2_0) = X1
| X1 != esk2_0
| ~ sorti1(X1)
| ~ sorti1(unit1) ),
inference(spm,[status(thm)],[33,19,theory(equality)]) ).
cnf(89,negated_conjecture,
( op1(j(X1),esk2_0) = j(X2)
| j(op2(X1,X2)) != esk2_0
| ~ sorti1(j(X2))
| ~ sorti1(j(X1))
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[33,61,theory(equality)]) ).
cnf(92,plain,
( op1(unit1,esk2_0) = X1
| X1 != esk2_0
| ~ sorti1(X1)
| $false ),
inference(rw,[status(thm)],[88,21,theory(equality)]) ).
cnf(93,plain,
( op1(unit1,esk2_0) = X1
| X1 != esk2_0
| ~ sorti1(X1) ),
inference(cn,[status(thm)],[92,theory(equality)]) ).
cnf(94,negated_conjecture,
( j(op2(h(X1),X2)) = op1(X1,j(X2))
| ~ sorti2(X2)
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[81,58]) ).
cnf(98,negated_conjecture,
( j(h(X1)) = op1(X1,j(unit2))
| ~ sorti2(unit2)
| ~ sorti1(X1)
| ~ sorti2(h(X1)) ),
inference(spm,[status(thm)],[94,41,theory(equality)]) ).
cnf(102,negated_conjecture,
( j(h(X1)) = op1(X1,j(unit2))
| $false
| ~ sorti1(X1)
| ~ sorti2(h(X1)) ),
inference(rw,[status(thm)],[98,20,theory(equality)]) ).
cnf(103,negated_conjecture,
( j(h(X1)) = op1(X1,j(unit2))
| ~ sorti1(X1)
| ~ sorti2(h(X1)) ),
inference(cn,[status(thm)],[102,theory(equality)]) ).
cnf(115,plain,
( op1(unit1,esk2_0) = esk2_0
| ~ sorti1(esk2_0) ),
inference(er,[status(thm)],[93,theory(equality)]) ).
cnf(116,plain,
( op1(unit1,esk2_0) = esk2_0
| $false ),
inference(rw,[status(thm)],[115,31,theory(equality)]) ).
cnf(117,plain,
op1(unit1,esk2_0) = esk2_0,
inference(cn,[status(thm)],[116,theory(equality)]) ).
cnf(129,negated_conjecture,
( j(h(X1)) = op1(X1,j(unit2))
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[103,58]) ).
cnf(133,negated_conjecture,
( op1(X1,j(unit2)) = X1
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[63,129,theory(equality)]) ).
cnf(136,negated_conjecture,
( unit1 = j(unit2)
| ~ sorti1(j(unit2))
| ~ sorti1(unit1) ),
inference(spm,[status(thm)],[19,133,theory(equality)]) ).
cnf(140,negated_conjecture,
( unit1 = j(unit2)
| ~ sorti1(j(unit2))
| $false ),
inference(rw,[status(thm)],[136,21,theory(equality)]) ).
cnf(141,negated_conjecture,
( unit1 = j(unit2)
| ~ sorti1(j(unit2)) ),
inference(cn,[status(thm)],[140,theory(equality)]) ).
cnf(144,negated_conjecture,
( j(unit2) = unit1
| ~ sorti2(unit2) ),
inference(spm,[status(thm)],[141,59,theory(equality)]) ).
cnf(145,negated_conjecture,
( j(unit2) = unit1
| $false ),
inference(rw,[status(thm)],[144,20,theory(equality)]) ).
cnf(146,negated_conjecture,
j(unit2) = unit1,
inference(cn,[status(thm)],[145,theory(equality)]) ).
cnf(148,negated_conjecture,
( h(unit1) = unit2
| ~ sorti2(unit2) ),
inference(spm,[status(thm)],[62,146,theory(equality)]) ).
cnf(155,negated_conjecture,
( j(h(X1)) = op1(X1,unit1)
| ~ sorti1(X1) ),
inference(rw,[status(thm)],[129,146,theory(equality)]) ).
cnf(159,negated_conjecture,
( h(unit1) = unit2
| $false ),
inference(rw,[status(thm)],[148,20,theory(equality)]) ).
cnf(160,negated_conjecture,
h(unit1) = unit2,
inference(cn,[status(thm)],[159,theory(equality)]) ).
cnf(167,negated_conjecture,
( op2(unit2,h(X1)) = h(op1(unit1,X1))
| ~ sorti1(X1)
| ~ sorti1(unit1) ),
inference(spm,[status(thm)],[60,160,theory(equality)]) ).
cnf(176,negated_conjecture,
( op2(unit2,h(X1)) = h(op1(unit1,X1))
| ~ sorti1(X1)
| $false ),
inference(rw,[status(thm)],[167,21,theory(equality)]) ).
cnf(177,negated_conjecture,
( op2(unit2,h(X1)) = h(op1(unit1,X1))
| ~ sorti1(X1) ),
inference(cn,[status(thm)],[176,theory(equality)]) ).
cnf(207,negated_conjecture,
( sorti2(h(op1(X1,X2)))
| ~ sorti2(h(X2))
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[86,58]) ).
cnf(208,negated_conjecture,
( sorti2(h(op1(X1,X2)))
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(csr,[status(thm)],[207,58]) ).
cnf(210,negated_conjecture,
( sorti2(h(esk2_0))
| ~ sorti1(esk2_0)
| ~ sorti1(unit1) ),
inference(spm,[status(thm)],[208,117,theory(equality)]) ).
cnf(217,negated_conjecture,
( sorti2(h(esk2_0))
| $false
| ~ sorti1(unit1) ),
inference(rw,[status(thm)],[210,31,theory(equality)]) ).
cnf(218,negated_conjecture,
( sorti2(h(esk2_0))
| $false
| $false ),
inference(rw,[status(thm)],[217,21,theory(equality)]) ).
cnf(219,negated_conjecture,
sorti2(h(esk2_0)),
inference(cn,[status(thm)],[218,theory(equality)]) ).
cnf(224,negated_conjecture,
( j(unit2) = op1(unit1,unit1)
| ~ sorti1(unit1) ),
inference(spm,[status(thm)],[155,160,theory(equality)]) ).
cnf(232,negated_conjecture,
( unit1 = op1(unit1,unit1)
| ~ sorti1(unit1) ),
inference(rw,[status(thm)],[224,146,theory(equality)]) ).
cnf(233,negated_conjecture,
( unit1 = op1(unit1,unit1)
| $false ),
inference(rw,[status(thm)],[232,21,theory(equality)]) ).
cnf(234,negated_conjecture,
unit1 = op1(unit1,unit1),
inference(cn,[status(thm)],[233,theory(equality)]) ).
cnf(261,negated_conjecture,
( j(op2(X1,h(X2))) = op1(j(X1),X2)
| ~ sorti2(X1)
| ~ sorti1(X2) ),
inference(csr,[status(thm)],[82,58]) ).
cnf(387,negated_conjecture,
( j(h(op1(unit1,X1))) = op1(j(unit2),X1)
| ~ sorti2(unit2)
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[261,177,theory(equality)]) ).
cnf(395,negated_conjecture,
( j(h(op1(unit1,X1))) = op1(unit1,X1)
| ~ sorti2(unit2)
| ~ sorti1(X1) ),
inference(rw,[status(thm)],[387,146,theory(equality)]) ).
cnf(396,negated_conjecture,
( j(h(op1(unit1,X1))) = op1(unit1,X1)
| $false
| ~ sorti1(X1) ),
inference(rw,[status(thm)],[395,20,theory(equality)]) ).
cnf(397,negated_conjecture,
( j(h(op1(unit1,X1))) = op1(unit1,X1)
| ~ sorti1(X1) ),
inference(cn,[status(thm)],[396,theory(equality)]) ).
cnf(492,negated_conjecture,
( h(op1(j(X1),X2)) = op2(X1,h(X2))
| ~ sorti2(X1)
| ~ sorti1(X2) ),
inference(csr,[status(thm)],[84,59]) ).
cnf(676,negated_conjecture,
( j(h(esk2_0)) = esk2_0
| ~ sorti1(esk2_0) ),
inference(spm,[status(thm)],[397,117,theory(equality)]) ).
cnf(696,negated_conjecture,
( j(h(esk2_0)) = esk2_0
| $false ),
inference(rw,[status(thm)],[676,31,theory(equality)]) ).
cnf(697,negated_conjecture,
j(h(esk2_0)) = esk2_0,
inference(cn,[status(thm)],[696,theory(equality)]) ).
cnf(1042,negated_conjecture,
( op1(j(X1),esk2_0) = j(X2)
| j(op2(X1,X2)) != esk2_0
| ~ sorti2(X2)
| ~ sorti2(X1)
| ~ sorti1(j(X2)) ),
inference(csr,[status(thm)],[89,59]) ).
cnf(1043,negated_conjecture,
( op1(j(X1),esk2_0) = j(X2)
| j(op2(X1,X2)) != esk2_0
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[1042,59]) ).
cnf(1049,negated_conjecture,
( op1(j(esk4_1(X1)),esk2_0) = j(esk5_1(X1))
| j(X1) != esk2_0
| ~ sorti2(esk5_1(X1))
| ~ sorti2(esk4_1(X1))
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[1043,52,theory(equality)]) ).
cnf(69916,negated_conjecture,
( op1(j(esk4_1(X1)),esk2_0) = j(esk5_1(X1))
| j(X1) != esk2_0
| ~ sorti2(esk5_1(X1))
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[1049,54]) ).
cnf(69917,negated_conjecture,
( op1(j(esk4_1(X1)),esk2_0) = j(esk5_1(X1))
| j(X1) != esk2_0
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[69916,53]) ).
cnf(69919,negated_conjecture,
( op1(j(esk4_1(h(esk2_0))),esk2_0) = j(esk5_1(h(esk2_0)))
| ~ sorti2(h(esk2_0)) ),
inference(spm,[status(thm)],[69917,697,theory(equality)]) ).
cnf(70005,negated_conjecture,
( op1(j(esk4_1(h(esk2_0))),esk2_0) = j(esk5_1(h(esk2_0)))
| $false ),
inference(rw,[status(thm)],[69919,219,theory(equality)]) ).
cnf(70006,negated_conjecture,
op1(j(esk4_1(h(esk2_0))),esk2_0) = j(esk5_1(h(esk2_0))),
inference(cn,[status(thm)],[70005,theory(equality)]) ).
cnf(70011,negated_conjecture,
( h(j(esk5_1(h(esk2_0)))) = op2(esk4_1(h(esk2_0)),h(esk2_0))
| ~ sorti2(esk4_1(h(esk2_0)))
| ~ sorti1(esk2_0) ),
inference(spm,[status(thm)],[492,70006,theory(equality)]) ).
cnf(70060,negated_conjecture,
( h(j(esk5_1(h(esk2_0)))) = op2(esk4_1(h(esk2_0)),h(esk2_0))
| ~ sorti2(esk4_1(h(esk2_0)))
| $false ),
inference(rw,[status(thm)],[70011,31,theory(equality)]) ).
cnf(70061,negated_conjecture,
( h(j(esk5_1(h(esk2_0)))) = op2(esk4_1(h(esk2_0)),h(esk2_0))
| ~ sorti2(esk4_1(h(esk2_0))) ),
inference(cn,[status(thm)],[70060,theory(equality)]) ).
cnf(89545,negated_conjecture,
( h(j(esk5_1(h(esk2_0)))) = op2(esk4_1(h(esk2_0)),h(esk2_0))
| ~ sorti2(h(esk2_0)) ),
inference(spm,[status(thm)],[70061,54,theory(equality)]) ).
cnf(89546,negated_conjecture,
( h(j(esk5_1(h(esk2_0)))) = op2(esk4_1(h(esk2_0)),h(esk2_0))
| $false ),
inference(rw,[status(thm)],[89545,219,theory(equality)]) ).
cnf(89547,negated_conjecture,
h(j(esk5_1(h(esk2_0)))) = op2(esk4_1(h(esk2_0)),h(esk2_0)),
inference(cn,[status(thm)],[89546,theory(equality)]) ).
cnf(89549,negated_conjecture,
( op2(esk4_1(h(esk2_0)),h(esk2_0)) = esk5_1(h(esk2_0))
| ~ sorti2(esk5_1(h(esk2_0))) ),
inference(spm,[status(thm)],[62,89547,theory(equality)]) ).
cnf(120818,negated_conjecture,
( op2(esk4_1(h(esk2_0)),h(esk2_0)) = esk5_1(h(esk2_0))
| ~ sorti2(h(esk2_0)) ),
inference(spm,[status(thm)],[89549,53,theory(equality)]) ).
cnf(120819,negated_conjecture,
( op2(esk4_1(h(esk2_0)),h(esk2_0)) = esk5_1(h(esk2_0))
| $false ),
inference(rw,[status(thm)],[120818,219,theory(equality)]) ).
cnf(120820,negated_conjecture,
op2(esk4_1(h(esk2_0)),h(esk2_0)) = esk5_1(h(esk2_0)),
inference(cn,[status(thm)],[120819,theory(equality)]) ).
cnf(120821,negated_conjecture,
( unit2 = h(esk2_0)
| ~ sorti2(h(esk2_0)) ),
inference(spm,[status(thm)],[51,120820,theory(equality)]) ).
cnf(120865,negated_conjecture,
( unit2 = h(esk2_0)
| $false ),
inference(rw,[status(thm)],[120821,219,theory(equality)]) ).
cnf(120866,negated_conjecture,
unit2 = h(esk2_0),
inference(cn,[status(thm)],[120865,theory(equality)]) ).
cnf(121195,negated_conjecture,
j(unit2) = esk2_0,
inference(rw,[status(thm)],[697,120866,theory(equality)]) ).
cnf(121196,negated_conjecture,
unit1 = esk2_0,
inference(rw,[status(thm)],[121195,146,theory(equality)]) ).
cnf(122044,plain,
( op1(X1,X2) != unit1
| esk2_0 != unit1
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(rw,[status(thm)],[32,121196,theory(equality)]) ).
cnf(122045,plain,
( op1(X1,X2) != unit1
| $false
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(rw,[status(thm)],[122044,121196,theory(equality)]) ).
cnf(122046,plain,
( op1(X1,X2) != unit1
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(cn,[status(thm)],[122045,theory(equality)]) ).
cnf(122047,negated_conjecture,
~ sorti1(unit1),
inference(spm,[status(thm)],[122046,234,theory(equality)]) ).
cnf(122157,negated_conjecture,
$false,
inference(rw,[status(thm)],[122047,21,theory(equality)]) ).
cnf(122158,negated_conjecture,
$false,
inference(cn,[status(thm)],[122157,theory(equality)]) ).
cnf(122159,negated_conjecture,
$false,
122158,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/ALG/ALG072+1.p
% --creating new selector for []
% -running prover on /tmp/tmpVtabsf/sel_ALG072+1.p_1 with time limit 29
% -prover status Theorem
% Problem ALG072+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/ALG/ALG072+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/ALG/ALG072+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
%
%------------------------------------------------------------------------------