%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GRP748+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 11:28:04 EST 2010
% Result : Theorem 0.44s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of formulae : 79 ( 60 unt; 0 def)
% Number of atoms : 108 ( 105 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 17 ~; 20 |; 9 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 13 con; 0-2 aty)
% Number of variables : 155 ( 0 sgn 62 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] : mult(X1,unit) = X1,
file('/tmp/tmpS7vjNR/sel_GRP748+1.p_1',f05) ).
fof(2,axiom,
! [X2,X1] : rd(mult(X1,X2),X2) = X1,
file('/tmp/tmpS7vjNR/sel_GRP748+1.p_1',f04) ).
fof(3,axiom,
! [X3,X2,X1] : mult(mult(mult(X1,X2),X3),X2) = mult(X1,mult(mult(X2,X3),X2)),
file('/tmp/tmpS7vjNR/sel_GRP748+1.p_1',f07) ).
fof(4,axiom,
! [X1] : mult(unit,X1) = X1,
file('/tmp/tmpS7vjNR/sel_GRP748+1.p_1',f06) ).
fof(5,axiom,
! [X2,X1] : mult(X1,ld(X1,X2)) = X2,
file('/tmp/tmpS7vjNR/sel_GRP748+1.p_1',f01) ).
fof(6,conjecture,
( ! [X4,X5,X6] : mult(X6,mult(X4,mult(X6,X5))) = mult(mult(mult(X6,X4),X6),X5)
| ! [X7,X8,X9] : mult(X7,mult(X9,mult(X8,X9))) = mult(mult(mult(X7,X9),X8),X9)
| ! [X10,X11,X12] : mult(mult(X12,X10),mult(X11,X12)) = mult(mult(X12,mult(X10,X11)),X12)
| ! [X13,X14,X15] : mult(mult(X15,X13),mult(X14,X15)) = mult(X15,mult(mult(X13,X14),X15)) ),
file('/tmp/tmpS7vjNR/sel_GRP748+1.p_1',goals) ).
fof(7,axiom,
! [X2,X1] : mult(rd(X1,X2),X2) = X1,
file('/tmp/tmpS7vjNR/sel_GRP748+1.p_1',f03) ).
fof(8,axiom,
! [X2,X1] : ld(X1,mult(X1,X2)) = X2,
file('/tmp/tmpS7vjNR/sel_GRP748+1.p_1',f02) ).
fof(9,axiom,
! [X1] : mult(i(X1),X1) = unit,
file('/tmp/tmpS7vjNR/sel_GRP748+1.p_1',f10) ).
fof(10,axiom,
! [X2,X1] :
( mult(X1,X2) = mult(X2,X1)
| mult(i(X1),mult(X1,X2)) = X2 ),
file('/tmp/tmpS7vjNR/sel_GRP748+1.p_1',f11) ).
fof(11,axiom,
! [X1] : mult(X1,i(X1)) = unit,
file('/tmp/tmpS7vjNR/sel_GRP748+1.p_1',f09) ).
fof(12,axiom,
! [X2,X1] : mult(mult(X1,X2),i(X2)) = X1,
file('/tmp/tmpS7vjNR/sel_GRP748+1.p_1',f08) ).
fof(13,negated_conjecture,
~ ( ! [X4,X5,X6] : mult(X6,mult(X4,mult(X6,X5))) = mult(mult(mult(X6,X4),X6),X5)
| ! [X7,X8,X9] : mult(X7,mult(X9,mult(X8,X9))) = mult(mult(mult(X7,X9),X8),X9)
| ! [X10,X11,X12] : mult(mult(X12,X10),mult(X11,X12)) = mult(mult(X12,mult(X10,X11)),X12)
| ! [X13,X14,X15] : mult(mult(X15,X13),mult(X14,X15)) = mult(X15,mult(mult(X13,X14),X15)) ),
inference(assume_negation,[status(cth)],[6]) ).
fof(14,plain,
! [X2] : mult(X2,unit) = X2,
inference(variable_rename,[status(thm)],[1]) ).
cnf(15,plain,
mult(X1,unit) = X1,
inference(split_conjunct,[status(thm)],[14]) ).
fof(16,plain,
! [X3,X4] : rd(mult(X4,X3),X3) = X4,
inference(variable_rename,[status(thm)],[2]) ).
cnf(17,plain,
rd(mult(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[16]) ).
fof(18,plain,
! [X4,X5,X6] : mult(mult(mult(X6,X5),X4),X5) = mult(X6,mult(mult(X5,X4),X5)),
inference(variable_rename,[status(thm)],[3]) ).
cnf(19,plain,
mult(mult(mult(X1,X2),X3),X2) = mult(X1,mult(mult(X2,X3),X2)),
inference(split_conjunct,[status(thm)],[18]) ).
fof(20,plain,
! [X2] : mult(unit,X2) = X2,
inference(variable_rename,[status(thm)],[4]) ).
cnf(21,plain,
mult(unit,X1) = X1,
inference(split_conjunct,[status(thm)],[20]) ).
fof(22,plain,
! [X3,X4] : mult(X4,ld(X4,X3)) = X3,
inference(variable_rename,[status(thm)],[5]) ).
cnf(23,plain,
mult(X1,ld(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[22]) ).
fof(24,negated_conjecture,
( ? [X4,X5,X6] : mult(X6,mult(X4,mult(X6,X5))) != mult(mult(mult(X6,X4),X6),X5)
& ? [X7,X8,X9] : mult(X7,mult(X9,mult(X8,X9))) != mult(mult(mult(X7,X9),X8),X9)
& ? [X10,X11,X12] : mult(mult(X12,X10),mult(X11,X12)) != mult(mult(X12,mult(X10,X11)),X12)
& ? [X13,X14,X15] : mult(mult(X15,X13),mult(X14,X15)) != mult(X15,mult(mult(X13,X14),X15)) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(25,negated_conjecture,
( ? [X16,X17,X18] : mult(X18,mult(X16,mult(X18,X17))) != mult(mult(mult(X18,X16),X18),X17)
& ? [X19,X20,X21] : mult(X19,mult(X21,mult(X20,X21))) != mult(mult(mult(X19,X21),X20),X21)
& ? [X22,X23,X24] : mult(mult(X24,X22),mult(X23,X24)) != mult(mult(X24,mult(X22,X23)),X24)
& ? [X25,X26,X27] : mult(mult(X27,X25),mult(X26,X27)) != mult(X27,mult(mult(X25,X26),X27)) ),
inference(variable_rename,[status(thm)],[24]) ).
fof(26,negated_conjecture,
( mult(esk3_0,mult(esk1_0,mult(esk3_0,esk2_0))) != mult(mult(mult(esk3_0,esk1_0),esk3_0),esk2_0)
& mult(esk4_0,mult(esk6_0,mult(esk5_0,esk6_0))) != mult(mult(mult(esk4_0,esk6_0),esk5_0),esk6_0)
& mult(mult(esk9_0,esk7_0),mult(esk8_0,esk9_0)) != mult(mult(esk9_0,mult(esk7_0,esk8_0)),esk9_0)
& mult(mult(esk12_0,esk10_0),mult(esk11_0,esk12_0)) != mult(esk12_0,mult(mult(esk10_0,esk11_0),esk12_0)) ),
inference(skolemize,[status(esa)],[25]) ).
cnf(29,negated_conjecture,
mult(esk4_0,mult(esk6_0,mult(esk5_0,esk6_0))) != mult(mult(mult(esk4_0,esk6_0),esk5_0),esk6_0),
inference(split_conjunct,[status(thm)],[26]) ).
fof(31,plain,
! [X3,X4] : mult(rd(X4,X3),X3) = X4,
inference(variable_rename,[status(thm)],[7]) ).
cnf(32,plain,
mult(rd(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[31]) ).
fof(33,plain,
! [X3,X4] : ld(X4,mult(X4,X3)) = X3,
inference(variable_rename,[status(thm)],[8]) ).
cnf(34,plain,
ld(X1,mult(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[33]) ).
fof(35,plain,
! [X2] : mult(i(X2),X2) = unit,
inference(variable_rename,[status(thm)],[9]) ).
cnf(36,plain,
mult(i(X1),X1) = unit,
inference(split_conjunct,[status(thm)],[35]) ).
fof(37,plain,
! [X3,X4] :
( mult(X4,X3) = mult(X3,X4)
| mult(i(X4),mult(X4,X3)) = X3 ),
inference(variable_rename,[status(thm)],[10]) ).
cnf(38,plain,
( mult(i(X1),mult(X1,X2)) = X2
| mult(X1,X2) = mult(X2,X1) ),
inference(split_conjunct,[status(thm)],[37]) ).
fof(39,plain,
! [X2] : mult(X2,i(X2)) = unit,
inference(variable_rename,[status(thm)],[11]) ).
cnf(40,plain,
mult(X1,i(X1)) = unit,
inference(split_conjunct,[status(thm)],[39]) ).
fof(41,plain,
! [X3,X4] : mult(mult(X4,X3),i(X3)) = X4,
inference(variable_rename,[status(thm)],[12]) ).
cnf(42,plain,
mult(mult(X1,X2),i(X2)) = X1,
inference(split_conjunct,[status(thm)],[41]) ).
cnf(48,plain,
ld(X1,unit) = i(X1),
inference(spm,[status(thm)],[34,40,theory(equality)]) ).
cnf(56,plain,
rd(X2,ld(X1,X2)) = X1,
inference(spm,[status(thm)],[17,23,theory(equality)]) ).
cnf(59,plain,
mult(unit,i(i(X1))) = X1,
inference(spm,[status(thm)],[42,40,theory(equality)]) ).
cnf(62,plain,
ld(mult(X1,X2),X1) = i(X2),
inference(spm,[status(thm)],[34,42,theory(equality)]) ).
cnf(63,plain,
mult(X1,i(X2)) = rd(X1,X2),
inference(spm,[status(thm)],[42,32,theory(equality)]) ).
cnf(67,plain,
i(i(X1)) = X1,
inference(rw,[status(thm)],[59,21,theory(equality)]) ).
cnf(73,plain,
( mult(i(X1),X2) = ld(X1,X2)
| X2 = mult(ld(X1,X2),X1) ),
inference(spm,[status(thm)],[38,23,theory(equality)]) ).
cnf(90,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(mult(X2,unit),X2)),
inference(spm,[status(thm)],[19,15,theory(equality)]) ).
cnf(94,plain,
mult(mult(unit,X2),X1) = mult(i(X1),mult(mult(X1,X2),X1)),
inference(spm,[status(thm)],[19,36,theory(equality)]) ).
cnf(95,plain,
mult(mult(X2,X3),ld(X1,X2)) = mult(X1,mult(mult(ld(X1,X2),X3),ld(X1,X2))),
inference(spm,[status(thm)],[19,23,theory(equality)]) ).
cnf(112,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[90,15,theory(equality)]) ).
cnf(116,plain,
mult(X2,X1) = mult(i(X1),mult(mult(X1,X2),X1)),
inference(rw,[status(thm)],[94,21,theory(equality)]) ).
cnf(119,negated_conjecture,
mult(esk4_0,mult(mult(esk6_0,esk5_0),esk6_0)) != mult(esk4_0,mult(esk6_0,mult(esk5_0,esk6_0))),
inference(rw,[status(thm)],[29,19,theory(equality)]) ).
cnf(151,plain,
( mult(X1,mult(i(X1),X2)) = X2
| mult(i(X1),X2) = mult(X2,i(X1)) ),
inference(spm,[status(thm)],[38,67,theory(equality)]) ).
cnf(201,plain,
rd(mult(X1,mult(X2,X2)),X2) = mult(X1,X2),
inference(spm,[status(thm)],[17,112,theory(equality)]) ).
cnf(293,plain,
rd(X1,i(X2)) = mult(X1,X2),
inference(spm,[status(thm)],[56,62,theory(equality)]) ).
cnf(452,plain,
( rd(X2,X1) = ld(X1,X2)
| mult(i(X1),X2) = ld(X1,X2) ),
inference(spm,[status(thm)],[17,73,theory(equality)]) ).
cnf(652,plain,
mult(i(X1),mult(X2,X1)) = mult(ld(X1,X2),X1),
inference(spm,[status(thm)],[116,23,theory(equality)]) ).
cnf(1649,plain,
mult(X1,mult(mult(i(X1),X2),i(X1))) = mult(mult(unit,X2),i(X1)),
inference(spm,[status(thm)],[95,48,theory(equality)]) ).
cnf(1686,plain,
mult(X1,rd(mult(i(X1),X2),X1)) = mult(mult(unit,X2),i(X1)),
inference(rw,[status(thm)],[1649,63,theory(equality)]) ).
cnf(1687,plain,
mult(X1,rd(mult(i(X1),X2),X1)) = rd(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1686,21,theory(equality)]),63,theory(equality)]) ).
cnf(5711,plain,
( mult(X1,mult(i(X1),X2)) = X2
| mult(i(X1),X2) = rd(X2,X1) ),
inference(rw,[status(thm)],[151,63,theory(equality)]) ).
cnf(6880,plain,
( rd(X2,i(X1)) = rd(rd(mult(i(i(X1)),X2),i(X1)),X1)
| mult(X1,rd(X2,i(X1))) = rd(mult(i(i(X1)),X2),i(X1)) ),
inference(spm,[status(thm)],[5711,1687,theory(equality)]) ).
cnf(6961,plain,
( mult(X2,X1) = rd(rd(mult(i(i(X1)),X2),i(X1)),X1)
| mult(X1,rd(X2,i(X1))) = rd(mult(i(i(X1)),X2),i(X1)) ),
inference(rw,[status(thm)],[6880,293,theory(equality)]) ).
cnf(6962,plain,
( mult(X2,X1) = mult(X1,X2)
| mult(X1,rd(X2,i(X1))) = rd(mult(i(i(X1)),X2),i(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[6961,67,theory(equality)]),293,theory(equality)]),17,theory(equality)]) ).
cnf(6963,plain,
( mult(X2,X1) = mult(X1,X2)
| mult(X1,mult(X2,X1)) = rd(mult(i(i(X1)),X2),i(X1)) ),
inference(rw,[status(thm)],[6962,293,theory(equality)]) ).
cnf(6964,plain,
( mult(X2,X1) = mult(X1,X2)
| mult(X1,mult(X2,X1)) = mult(mult(X1,X2),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[6963,67,theory(equality)]),293,theory(equality)]) ).
cnf(7059,negated_conjecture,
mult(esk5_0,esk6_0) = mult(esk6_0,esk5_0),
inference(spm,[status(thm)],[119,6964,theory(equality)]) ).
cnf(7185,negated_conjecture,
mult(mult(esk6_0,esk5_0),esk6_0) = mult(esk5_0,mult(esk6_0,esk6_0)),
inference(spm,[status(thm)],[112,7059,theory(equality)]) ).
cnf(7211,negated_conjecture,
mult(esk4_0,mult(mult(esk6_0,esk5_0),esk6_0)) != mult(esk4_0,mult(esk6_0,mult(esk6_0,esk5_0))),
inference(rw,[status(thm)],[119,7059,theory(equality)]) ).
cnf(7245,negated_conjecture,
mult(i(esk6_0),mult(esk5_0,mult(esk6_0,esk6_0))) = mult(ld(esk6_0,mult(esk6_0,esk5_0)),esk6_0),
inference(spm,[status(thm)],[652,7185,theory(equality)]) ).
cnf(7287,negated_conjecture,
mult(i(esk6_0),mult(esk5_0,mult(esk6_0,esk6_0))) = mult(esk6_0,esk5_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[7245,34,theory(equality)]),7059,theory(equality)]) ).
cnf(7323,negated_conjecture,
mult(esk4_0,mult(esk5_0,mult(esk6_0,esk6_0))) != mult(esk4_0,mult(esk6_0,mult(esk6_0,esk5_0))),
inference(rw,[status(thm)],[7211,7185,theory(equality)]) ).
cnf(8555,negated_conjecture,
( mult(esk6_0,esk5_0) = ld(esk6_0,mult(esk5_0,mult(esk6_0,esk6_0)))
| rd(mult(esk5_0,mult(esk6_0,esk6_0)),esk6_0) = ld(esk6_0,mult(esk5_0,mult(esk6_0,esk6_0))) ),
inference(spm,[status(thm)],[452,7287,theory(equality)]) ).
cnf(8591,negated_conjecture,
( mult(esk6_0,esk5_0) = ld(esk6_0,mult(esk5_0,mult(esk6_0,esk6_0)))
| mult(esk6_0,esk5_0) = ld(esk6_0,mult(esk5_0,mult(esk6_0,esk6_0))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[8555,201,theory(equality)]),7059,theory(equality)]) ).
cnf(8592,negated_conjecture,
mult(esk6_0,esk5_0) = ld(esk6_0,mult(esk5_0,mult(esk6_0,esk6_0))),
inference(cn,[status(thm)],[8591,theory(equality)]) ).
cnf(8712,negated_conjecture,
mult(esk6_0,mult(esk6_0,esk5_0)) = mult(esk5_0,mult(esk6_0,esk6_0)),
inference(spm,[status(thm)],[23,8592,theory(equality)]) ).
cnf(8775,negated_conjecture,
$false,
inference(rw,[status(thm)],[7323,8712,theory(equality)]) ).
cnf(8776,negated_conjecture,
$false,
inference(cn,[status(thm)],[8775,theory(equality)]) ).
cnf(8777,negated_conjecture,
$false,
8776,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRP/GRP748+1.p
% --creating new selector for []
% -running prover on /tmp/tmpS7vjNR/sel_GRP748+1.p_1 with time limit 29
% -prover status Theorem
% Problem GRP748+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRP/GRP748+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRP/GRP748+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
%
%------------------------------------------------------------------------------