TSTP Solution File: GRP775+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GRP775+1 : TPTP v5.0.0. Released v4.1.0.
% 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 11:33:29 EST 2010
% Result : Theorem 0.52s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 6
% Syntax : Number of formulae : 132 ( 26 unt; 0 def)
% Number of atoms : 342 ( 158 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 365 ( 155 ~; 170 |; 35 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 203 ( 3 sgn 45 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1,X2] :
( d(X1,X2)
<=> ( product(X1,product(X2,X1)) = X1
& product(X2,product(X1,X2)) = X2 ) ),
file('/tmp/tmpavXKju/sel_GRP775+1.p_1',goals) ).
fof(2,axiom,
! [X3,X4] :
( r(X3,X4)
<=> ( product(X3,X4) = X4
& product(X4,X3) = X3 ) ),
file('/tmp/tmpavXKju/sel_GRP775+1.p_1',sos04) ).
fof(3,axiom,
! [X5,X6] :
( d(X5,X6)
<=> ? [X7] :
( r(X5,X7)
& l(X7,X6) ) ),
file('/tmp/tmpavXKju/sel_GRP775+1.p_1',sos05) ).
fof(4,axiom,
! [X8,X9,X10] : product(product(X10,X9),X8) = product(X10,product(X9,X8)),
file('/tmp/tmpavXKju/sel_GRP775+1.p_1',sos01) ).
fof(5,axiom,
! [X10] : product(X10,X10) = X10,
file('/tmp/tmpavXKju/sel_GRP775+1.p_1',sos02) ).
fof(6,axiom,
! [X11,X12] :
( l(X11,X12)
<=> ( product(X11,X12) = X11
& product(X12,X11) = X12 ) ),
file('/tmp/tmpavXKju/sel_GRP775+1.p_1',sos03) ).
fof(7,negated_conjecture,
~ ! [X1,X2] :
( d(X1,X2)
<=> ( product(X1,product(X2,X1)) = X1
& product(X2,product(X1,X2)) = X2 ) ),
inference(assume_negation,[status(cth)],[1]) ).
fof(8,negated_conjecture,
? [X1,X2] :
( ( ~ d(X1,X2)
| product(X1,product(X2,X1)) != X1
| product(X2,product(X1,X2)) != X2 )
& ( d(X1,X2)
| ( product(X1,product(X2,X1)) = X1
& product(X2,product(X1,X2)) = X2 ) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(9,negated_conjecture,
? [X3,X4] :
( ( ~ d(X3,X4)
| product(X3,product(X4,X3)) != X3
| product(X4,product(X3,X4)) != X4 )
& ( d(X3,X4)
| ( product(X3,product(X4,X3)) = X3
& product(X4,product(X3,X4)) = X4 ) ) ),
inference(variable_rename,[status(thm)],[8]) ).
fof(10,negated_conjecture,
( ( ~ d(esk1_0,esk2_0)
| product(esk1_0,product(esk2_0,esk1_0)) != esk1_0
| product(esk2_0,product(esk1_0,esk2_0)) != esk2_0 )
& ( d(esk1_0,esk2_0)
| ( product(esk1_0,product(esk2_0,esk1_0)) = esk1_0
& product(esk2_0,product(esk1_0,esk2_0)) = esk2_0 ) ) ),
inference(skolemize,[status(esa)],[9]) ).
fof(11,negated_conjecture,
( ( ~ d(esk1_0,esk2_0)
| product(esk1_0,product(esk2_0,esk1_0)) != esk1_0
| product(esk2_0,product(esk1_0,esk2_0)) != esk2_0 )
& ( product(esk1_0,product(esk2_0,esk1_0)) = esk1_0
| d(esk1_0,esk2_0) )
& ( product(esk2_0,product(esk1_0,esk2_0)) = esk2_0
| d(esk1_0,esk2_0) ) ),
inference(distribute,[status(thm)],[10]) ).
cnf(12,negated_conjecture,
( d(esk1_0,esk2_0)
| product(esk2_0,product(esk1_0,esk2_0)) = esk2_0 ),
inference(split_conjunct,[status(thm)],[11]) ).
cnf(13,negated_conjecture,
( d(esk1_0,esk2_0)
| product(esk1_0,product(esk2_0,esk1_0)) = esk1_0 ),
inference(split_conjunct,[status(thm)],[11]) ).
cnf(14,negated_conjecture,
( product(esk2_0,product(esk1_0,esk2_0)) != esk2_0
| product(esk1_0,product(esk2_0,esk1_0)) != esk1_0
| ~ d(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[11]) ).
fof(15,plain,
! [X3,X4] :
( ( ~ r(X3,X4)
| ( product(X3,X4) = X4
& product(X4,X3) = X3 ) )
& ( product(X3,X4) != X4
| product(X4,X3) != X3
| r(X3,X4) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(16,plain,
! [X5,X6] :
( ( ~ r(X5,X6)
| ( product(X5,X6) = X6
& product(X6,X5) = X5 ) )
& ( product(X5,X6) != X6
| product(X6,X5) != X5
| r(X5,X6) ) ),
inference(variable_rename,[status(thm)],[15]) ).
fof(17,plain,
! [X5,X6] :
( ( product(X5,X6) = X6
| ~ r(X5,X6) )
& ( product(X6,X5) = X5
| ~ r(X5,X6) )
& ( product(X5,X6) != X6
| product(X6,X5) != X5
| r(X5,X6) ) ),
inference(distribute,[status(thm)],[16]) ).
cnf(18,plain,
( r(X1,X2)
| product(X2,X1) != X1
| product(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(19,plain,
( product(X2,X1) = X1
| ~ r(X1,X2) ),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(20,plain,
( product(X1,X2) = X2
| ~ r(X1,X2) ),
inference(split_conjunct,[status(thm)],[17]) ).
fof(21,plain,
! [X5,X6] :
( ( ~ d(X5,X6)
| ? [X7] :
( r(X5,X7)
& l(X7,X6) ) )
& ( ! [X7] :
( ~ r(X5,X7)
| ~ l(X7,X6) )
| d(X5,X6) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(22,plain,
! [X8,X9] :
( ( ~ d(X8,X9)
| ? [X10] :
( r(X8,X10)
& l(X10,X9) ) )
& ( ! [X11] :
( ~ r(X8,X11)
| ~ l(X11,X9) )
| d(X8,X9) ) ),
inference(variable_rename,[status(thm)],[21]) ).
fof(23,plain,
! [X8,X9] :
( ( ~ d(X8,X9)
| ( r(X8,esk3_2(X8,X9))
& l(esk3_2(X8,X9),X9) ) )
& ( ! [X11] :
( ~ r(X8,X11)
| ~ l(X11,X9) )
| d(X8,X9) ) ),
inference(skolemize,[status(esa)],[22]) ).
fof(24,plain,
! [X8,X9,X11] :
( ( ~ r(X8,X11)
| ~ l(X11,X9)
| d(X8,X9) )
& ( ~ d(X8,X9)
| ( r(X8,esk3_2(X8,X9))
& l(esk3_2(X8,X9),X9) ) ) ),
inference(shift_quantors,[status(thm)],[23]) ).
fof(25,plain,
! [X8,X9,X11] :
( ( ~ r(X8,X11)
| ~ l(X11,X9)
| d(X8,X9) )
& ( r(X8,esk3_2(X8,X9))
| ~ d(X8,X9) )
& ( l(esk3_2(X8,X9),X9)
| ~ d(X8,X9) ) ),
inference(distribute,[status(thm)],[24]) ).
cnf(26,plain,
( l(esk3_2(X1,X2),X2)
| ~ d(X1,X2) ),
inference(split_conjunct,[status(thm)],[25]) ).
cnf(27,plain,
( r(X1,esk3_2(X1,X2))
| ~ d(X1,X2) ),
inference(split_conjunct,[status(thm)],[25]) ).
cnf(28,plain,
( d(X1,X2)
| ~ l(X3,X2)
| ~ r(X1,X3) ),
inference(split_conjunct,[status(thm)],[25]) ).
fof(29,plain,
! [X11,X12,X13] : product(product(X13,X12),X11) = product(X13,product(X12,X11)),
inference(variable_rename,[status(thm)],[4]) ).
cnf(30,plain,
product(product(X1,X2),X3) = product(X1,product(X2,X3)),
inference(split_conjunct,[status(thm)],[29]) ).
fof(31,plain,
! [X11] : product(X11,X11) = X11,
inference(variable_rename,[status(thm)],[5]) ).
cnf(32,plain,
product(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[31]) ).
fof(33,plain,
! [X11,X12] :
( ( ~ l(X11,X12)
| ( product(X11,X12) = X11
& product(X12,X11) = X12 ) )
& ( product(X11,X12) != X11
| product(X12,X11) != X12
| l(X11,X12) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(34,plain,
! [X13,X14] :
( ( ~ l(X13,X14)
| ( product(X13,X14) = X13
& product(X14,X13) = X14 ) )
& ( product(X13,X14) != X13
| product(X14,X13) != X14
| l(X13,X14) ) ),
inference(variable_rename,[status(thm)],[33]) ).
fof(35,plain,
! [X13,X14] :
( ( product(X13,X14) = X13
| ~ l(X13,X14) )
& ( product(X14,X13) = X14
| ~ l(X13,X14) )
& ( product(X13,X14) != X13
| product(X14,X13) != X14
| l(X13,X14) ) ),
inference(distribute,[status(thm)],[34]) ).
cnf(36,plain,
( l(X1,X2)
| product(X2,X1) != X2
| product(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(37,plain,
( product(X2,X1) = X2
| ~ l(X1,X2) ),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(38,plain,
( product(X1,X2) = X1
| ~ l(X1,X2) ),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(39,plain,
( product(esk3_2(X1,X2),X1) = X1
| ~ d(X1,X2) ),
inference(spm,[status(thm)],[19,27,theory(equality)]) ).
cnf(40,plain,
( product(X1,esk3_2(X1,X2)) = esk3_2(X1,X2)
| ~ d(X1,X2) ),
inference(spm,[status(thm)],[20,27,theory(equality)]) ).
cnf(41,plain,
product(X1,product(X2,product(X1,X2))) = product(X1,X2),
inference(spm,[status(thm)],[32,30,theory(equality)]) ).
cnf(42,plain,
product(X1,X2) = product(X1,product(X1,X2)),
inference(spm,[status(thm)],[30,32,theory(equality)]) ).
cnf(48,plain,
( product(X1,esk3_2(X2,X1)) = X1
| ~ d(X2,X1) ),
inference(spm,[status(thm)],[37,26,theory(equality)]) ).
cnf(49,plain,
( product(esk3_2(X1,X2),X2) = esk3_2(X1,X2)
| ~ d(X1,X2) ),
inference(spm,[status(thm)],[38,26,theory(equality)]) ).
cnf(50,plain,
( d(X1,X2)
| ~ r(X1,esk3_2(X3,X2))
| ~ d(X3,X2) ),
inference(spm,[status(thm)],[28,26,theory(equality)]) ).
cnf(55,plain,
( d(X1,X2)
| ~ r(X1,X3)
| product(X2,X3) != X2
| product(X3,X2) != X3 ),
inference(spm,[status(thm)],[28,36,theory(equality)]) ).
cnf(58,plain,
product(product(X1,X2),X3) = product(X1,product(X2,product(product(X1,X2),X3))),
inference(spm,[status(thm)],[30,42,theory(equality)]) ).
cnf(64,plain,
product(X1,product(X2,X3)) = product(X1,product(X2,product(product(X1,X2),X3))),
inference(rw,[status(thm)],[58,30,theory(equality)]) ).
cnf(65,plain,
product(X1,product(X2,X3)) = product(X1,product(X2,product(X1,product(X2,X3)))),
inference(rw,[status(thm)],[64,30,theory(equality)]) ).
cnf(68,plain,
( product(X1,X3) = product(esk3_2(X1,X2),product(X1,X3))
| ~ d(X1,X2) ),
inference(spm,[status(thm)],[30,39,theory(equality)]) ).
cnf(127,plain,
( d(X1,X2)
| ~ d(X3,X2)
| product(esk3_2(X3,X2),X1) != X1
| product(X1,esk3_2(X3,X2)) != esk3_2(X3,X2) ),
inference(spm,[status(thm)],[50,18,theory(equality)]) ).
cnf(132,plain,
( product(esk3_2(X1,X2),product(X2,esk3_2(X1,X2))) = esk3_2(X1,X2)
| ~ d(X1,X2) ),
inference(spm,[status(thm)],[41,49,theory(equality)]) ).
cnf(162,plain,
( product(X1,X2) = esk3_2(X1,product(X1,X2))
| ~ d(X1,product(X1,X2)) ),
inference(spm,[status(thm)],[49,68,theory(equality)]) ).
cnf(174,plain,
( d(X1,X2)
| product(X2,X2) != X2
| ~ r(X1,X2) ),
inference(spm,[status(thm)],[55,32,theory(equality)]) ).
cnf(184,plain,
( d(X1,X2)
| $false
| ~ r(X1,X2) ),
inference(rw,[status(thm)],[174,32,theory(equality)]) ).
cnf(185,plain,
( d(X1,X2)
| ~ r(X1,X2) ),
inference(cn,[status(thm)],[184,theory(equality)]) ).
cnf(192,plain,
( d(X1,X2)
| product(X2,X1) != X1
| product(X1,X2) != X2 ),
inference(spm,[status(thm)],[185,18,theory(equality)]) ).
cnf(200,plain,
( r(X1,product(X1,X2))
| ~ d(X1,product(X1,X2)) ),
inference(spm,[status(thm)],[27,162,theory(equality)]) ).
cnf(202,plain,
( product(product(X1,X2),X1) = X1
| ~ d(X1,product(X1,X2)) ),
inference(spm,[status(thm)],[39,162,theory(equality)]) ).
cnf(213,plain,
( product(product(X1,X2),product(X1,X3)) = product(X1,X3)
| ~ d(X1,product(X1,X2)) ),
inference(spm,[status(thm)],[68,162,theory(equality)]) ).
cnf(216,plain,
( product(X1,product(X2,X1)) = X1
| ~ d(X1,product(X1,X2)) ),
inference(rw,[status(thm)],[202,30,theory(equality)]) ).
cnf(221,plain,
( product(X1,product(X2,product(X1,X3))) = product(X1,X3)
| ~ d(X1,product(X1,X2)) ),
inference(rw,[status(thm)],[213,30,theory(equality)]) ).
cnf(257,plain,
( product(X1,product(X2,product(X1,esk3_2(X2,X3)))) = product(X1,esk3_2(X2,X3))
| ~ d(X2,X3) ),
inference(spm,[status(thm)],[65,40,theory(equality)]) ).
cnf(264,plain,
( product(X1,product(esk3_2(X2,X3),product(X1,product(X2,X4)))) = product(X1,product(X2,X4))
| ~ d(X2,X3) ),
inference(spm,[status(thm)],[65,68,theory(equality)]) ).
cnf(300,plain,
( product(product(X1,X2),product(X3,product(X1,X2))) = product(X1,X2)
| ~ d(product(X1,X2),product(X1,product(X2,X3))) ),
inference(spm,[status(thm)],[216,30,theory(equality)]) ).
cnf(312,plain,
( product(X1,product(X2,product(X3,product(X1,X2)))) = product(X1,X2)
| ~ d(product(X1,X2),product(X1,product(X2,X3))) ),
inference(rw,[status(thm)],[300,30,theory(equality)]) ).
cnf(997,plain,
( d(esk3_2(X1,X2),X2)
| product(esk3_2(X1,X2),esk3_2(X1,X2)) != esk3_2(X1,X2)
| ~ d(X1,X2) ),
inference(spm,[status(thm)],[127,32,theory(equality)]) ).
cnf(1016,plain,
( d(esk3_2(X1,X2),X2)
| $false
| ~ d(X1,X2) ),
inference(rw,[status(thm)],[997,32,theory(equality)]) ).
cnf(1017,plain,
( d(esk3_2(X1,X2),X2)
| ~ d(X1,X2) ),
inference(cn,[status(thm)],[1016,theory(equality)]) ).
cnf(1032,plain,
( d(product(X1,X2),product(X1,X2))
| ~ d(X1,product(X1,X2)) ),
inference(spm,[status(thm)],[1017,162,theory(equality)]) ).
cnf(1103,plain,
( d(X1,X1)
| ~ d(esk3_2(X1,X2),X1)
| ~ d(X1,X2) ),
inference(spm,[status(thm)],[1032,39,theory(equality)]) ).
cnf(1117,plain,
( d(X1,X1)
| ~ d(product(X1,X2),X1)
| ~ d(X1,product(X1,X2)) ),
inference(spm,[status(thm)],[1103,162,theory(equality)]) ).
cnf(1132,plain,
( d(X1,X1)
| ~ d(X1,product(X1,X2))
| product(X1,product(X1,X2)) != product(X1,X2)
| product(product(X1,X2),X1) != X1 ),
inference(spm,[status(thm)],[1117,192,theory(equality)]) ).
cnf(1138,plain,
( d(X1,X1)
| ~ d(X1,product(X1,X2))
| $false
| product(product(X1,X2),X1) != X1 ),
inference(rw,[status(thm)],[1132,42,theory(equality)]) ).
cnf(1139,plain,
( d(X1,X1)
| ~ d(X1,product(X1,X2))
| $false
| product(X1,product(X2,X1)) != X1 ),
inference(rw,[status(thm)],[1138,30,theory(equality)]) ).
cnf(1140,plain,
( d(X1,X1)
| ~ d(X1,product(X1,X2))
| product(X1,product(X2,X1)) != X1 ),
inference(cn,[status(thm)],[1139,theory(equality)]) ).
cnf(1141,plain,
( d(X1,X1)
| ~ d(X1,product(X1,X2)) ),
inference(csr,[status(thm)],[1140,216]) ).
cnf(1154,plain,
( d(X1,X1)
| product(product(X1,X2),X1) != X1
| product(X1,product(X1,X2)) != product(X1,X2) ),
inference(spm,[status(thm)],[1141,192,theory(equality)]) ).
cnf(1160,plain,
( d(X1,X1)
| product(X1,product(X2,X1)) != X1
| product(X1,product(X1,X2)) != product(X1,X2) ),
inference(rw,[status(thm)],[1154,30,theory(equality)]) ).
cnf(1161,plain,
( d(X1,X1)
| product(X1,product(X2,X1)) != X1
| $false ),
inference(rw,[status(thm)],[1160,42,theory(equality)]) ).
cnf(1162,plain,
( d(X1,X1)
| product(X1,product(X2,X1)) != X1 ),
inference(cn,[status(thm)],[1161,theory(equality)]) ).
cnf(1242,plain,
( d(X1,X1)
| product(X1,X1) != X1 ),
inference(spm,[status(thm)],[1162,32,theory(equality)]) ).
cnf(1268,plain,
( d(X1,X1)
| $false ),
inference(rw,[status(thm)],[1242,32,theory(equality)]) ).
cnf(1269,plain,
d(X1,X1),
inference(cn,[status(thm)],[1268,theory(equality)]) ).
cnf(4615,plain,
( product(X1,product(X2,product(X1,X3))) = product(X1,X3)
| product(product(X1,X2),X1) != X1
| product(X1,product(X1,X2)) != product(X1,X2) ),
inference(spm,[status(thm)],[221,192,theory(equality)]) ).
cnf(4652,plain,
( product(X1,product(X2,product(X1,X3))) = product(X1,X3)
| product(X1,product(X2,X1)) != X1
| product(X1,product(X1,X2)) != product(X1,X2) ),
inference(rw,[status(thm)],[4615,30,theory(equality)]) ).
cnf(4653,plain,
( product(X1,product(X2,product(X1,X3))) = product(X1,X3)
| product(X1,product(X2,X1)) != X1
| $false ),
inference(rw,[status(thm)],[4652,42,theory(equality)]) ).
cnf(4654,plain,
( product(X1,product(X2,product(X1,X3))) = product(X1,X3)
| product(X1,product(X2,X1)) != X1 ),
inference(cn,[status(thm)],[4653,theory(equality)]) ).
cnf(6511,plain,
( product(X1,product(X2,X1)) = X1
| ~ d(X2,X1) ),
inference(spm,[status(thm)],[257,48,theory(equality)]) ).
cnf(6685,negated_conjecture,
product(esk2_0,product(esk1_0,esk2_0)) = esk2_0,
inference(spm,[status(thm)],[6511,12,theory(equality)]) ).
cnf(6719,negated_conjecture,
( d(X1,esk2_0)
| product(product(esk1_0,esk2_0),esk2_0) != product(esk1_0,esk2_0)
| ~ r(X1,product(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[55,6685,theory(equality)]) ).
cnf(6764,negated_conjecture,
( product(esk2_0,product(product(esk1_0,esk2_0),product(esk2_0,X1))) = product(esk2_0,X1)
| ~ d(esk2_0,esk2_0) ),
inference(spm,[status(thm)],[221,6685,theory(equality)]) ).
cnf(6783,negated_conjecture,
( product(esk1_0,product(esk2_0,esk1_0)) != esk1_0
| $false
| ~ d(esk1_0,esk2_0) ),
inference(rw,[status(thm)],[14,6685,theory(equality)]) ).
cnf(6784,negated_conjecture,
( product(esk1_0,product(esk2_0,esk1_0)) != esk1_0
| ~ d(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[6783,theory(equality)]) ).
cnf(6794,negated_conjecture,
( d(X1,esk2_0)
| $false
| ~ r(X1,product(esk1_0,esk2_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[6719,30,theory(equality)]),32,theory(equality)]) ).
cnf(6795,negated_conjecture,
( d(X1,esk2_0)
| ~ r(X1,product(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[6794,theory(equality)]) ).
cnf(6855,negated_conjecture,
( product(esk2_0,product(esk1_0,product(esk2_0,X1))) = product(esk2_0,X1)
| ~ d(esk2_0,esk2_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[6764,30,theory(equality)]),42,theory(equality)]) ).
cnf(6856,negated_conjecture,
( product(esk2_0,product(esk1_0,product(esk2_0,X1))) = product(esk2_0,X1)
| $false ),
inference(rw,[status(thm)],[6855,1269,theory(equality)]) ).
cnf(6857,negated_conjecture,
product(esk2_0,product(esk1_0,product(esk2_0,X1))) = product(esk2_0,X1),
inference(cn,[status(thm)],[6856,theory(equality)]) ).
cnf(7532,negated_conjecture,
( d(esk1_0,esk2_0)
| ~ d(esk1_0,product(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[6795,200,theory(equality)]) ).
cnf(7546,negated_conjecture,
( d(esk1_0,esk2_0)
| product(product(esk1_0,esk2_0),esk1_0) != esk1_0
| product(esk1_0,product(esk1_0,esk2_0)) != product(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[7532,192,theory(equality)]) ).
cnf(7548,negated_conjecture,
( d(esk1_0,esk2_0)
| product(esk1_0,product(esk2_0,esk1_0)) != esk1_0
| product(esk1_0,product(esk1_0,esk2_0)) != product(esk1_0,esk2_0) ),
inference(rw,[status(thm)],[7546,30,theory(equality)]) ).
cnf(7549,negated_conjecture,
( d(esk1_0,esk2_0)
| product(esk1_0,product(esk2_0,esk1_0)) != esk1_0
| $false ),
inference(rw,[status(thm)],[7548,42,theory(equality)]) ).
cnf(7550,negated_conjecture,
( d(esk1_0,esk2_0)
| product(esk1_0,product(esk2_0,esk1_0)) != esk1_0 ),
inference(cn,[status(thm)],[7549,theory(equality)]) ).
cnf(7551,negated_conjecture,
d(esk1_0,esk2_0),
inference(csr,[status(thm)],[7550,13]) ).
cnf(7554,negated_conjecture,
( product(esk1_0,product(esk2_0,esk1_0)) != esk1_0
| $false ),
inference(rw,[status(thm)],[6784,7551,theory(equality)]) ).
cnf(7555,negated_conjecture,
product(esk1_0,product(esk2_0,esk1_0)) != esk1_0,
inference(cn,[status(thm)],[7554,theory(equality)]) ).
cnf(7598,negated_conjecture,
( product(esk2_0,product(esk3_2(esk1_0,X1),esk2_0)) = esk2_0
| ~ d(esk1_0,X1) ),
inference(spm,[status(thm)],[264,6685,theory(equality)]) ).
cnf(8566,negated_conjecture,
( product(esk2_0,esk3_2(esk1_0,esk2_0)) = esk2_0
| ~ d(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[7598,49,theory(equality)]) ).
cnf(8651,negated_conjecture,
( product(esk2_0,esk3_2(esk1_0,esk2_0)) = esk2_0
| $false ),
inference(rw,[status(thm)],[8566,7551,theory(equality)]) ).
cnf(8652,negated_conjecture,
product(esk2_0,esk3_2(esk1_0,esk2_0)) = esk2_0,
inference(cn,[status(thm)],[8651,theory(equality)]) ).
cnf(8767,negated_conjecture,
( product(esk3_2(esk1_0,esk2_0),esk2_0) = esk3_2(esk1_0,esk2_0)
| ~ d(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[132,8652,theory(equality)]) ).
cnf(8824,negated_conjecture,
( product(esk3_2(esk1_0,esk2_0),esk2_0) = esk3_2(esk1_0,esk2_0)
| $false ),
inference(rw,[status(thm)],[8767,7551,theory(equality)]) ).
cnf(8825,negated_conjecture,
product(esk3_2(esk1_0,esk2_0),esk2_0) = esk3_2(esk1_0,esk2_0),
inference(cn,[status(thm)],[8824,theory(equality)]) ).
cnf(9087,negated_conjecture,
( product(X1,product(esk2_0,product(esk3_2(esk1_0,esk2_0),product(X1,esk2_0)))) = product(X1,esk2_0)
| ~ d(product(X1,esk2_0),product(X1,esk2_0)) ),
inference(spm,[status(thm)],[312,8652,theory(equality)]) ).
cnf(9225,negated_conjecture,
( product(X1,product(esk2_0,product(esk3_2(esk1_0,esk2_0),product(X1,esk2_0)))) = product(X1,esk2_0)
| $false ),
inference(rw,[status(thm)],[9087,1269,theory(equality)]) ).
cnf(9226,negated_conjecture,
product(X1,product(esk2_0,product(esk3_2(esk1_0,esk2_0),product(X1,esk2_0)))) = product(X1,esk2_0),
inference(cn,[status(thm)],[9225,theory(equality)]) ).
cnf(10118,negated_conjecture,
product(esk2_0,product(esk1_0,esk2_0)) = product(esk2_0,product(esk3_2(esk1_0,esk2_0),product(esk1_0,esk2_0))),
inference(spm,[status(thm)],[6857,9226,theory(equality)]) ).
cnf(10236,negated_conjecture,
esk2_0 = product(esk2_0,product(esk3_2(esk1_0,esk2_0),product(esk1_0,esk2_0))),
inference(rw,[status(thm)],[10118,6685,theory(equality)]) ).
cnf(10395,negated_conjecture,
( product(esk3_2(esk1_0,esk2_0),esk2_0) = product(esk3_2(esk1_0,esk2_0),product(esk1_0,esk2_0))
| product(esk3_2(esk1_0,esk2_0),product(esk2_0,esk3_2(esk1_0,esk2_0))) != esk3_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[4654,10236,theory(equality)]) ).
cnf(10499,negated_conjecture,
( esk3_2(esk1_0,esk2_0) = product(esk3_2(esk1_0,esk2_0),product(esk1_0,esk2_0))
| product(esk3_2(esk1_0,esk2_0),product(esk2_0,esk3_2(esk1_0,esk2_0))) != esk3_2(esk1_0,esk2_0) ),
inference(rw,[status(thm)],[10395,8825,theory(equality)]) ).
cnf(10500,negated_conjecture,
( esk3_2(esk1_0,esk2_0) = product(esk3_2(esk1_0,esk2_0),product(esk1_0,esk2_0))
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[10499,8652,theory(equality)]),8825,theory(equality)]) ).
cnf(10501,negated_conjecture,
esk3_2(esk1_0,esk2_0) = product(esk3_2(esk1_0,esk2_0),product(esk1_0,esk2_0)),
inference(cn,[status(thm)],[10500,theory(equality)]) ).
cnf(10788,negated_conjecture,
( esk3_2(esk1_0,esk2_0) = product(esk1_0,esk2_0)
| ~ d(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[68,10501,theory(equality)]) ).
cnf(10870,negated_conjecture,
( esk3_2(esk1_0,esk2_0) = product(esk1_0,esk2_0)
| $false ),
inference(rw,[status(thm)],[10788,7551,theory(equality)]) ).
cnf(10871,negated_conjecture,
esk3_2(esk1_0,esk2_0) = product(esk1_0,esk2_0),
inference(cn,[status(thm)],[10870,theory(equality)]) ).
cnf(10988,negated_conjecture,
( product(product(esk1_0,esk2_0),esk1_0) = esk1_0
| ~ d(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[39,10871,theory(equality)]) ).
cnf(11059,negated_conjecture,
( product(esk1_0,product(esk2_0,esk1_0)) = esk1_0
| ~ d(esk1_0,esk2_0) ),
inference(rw,[status(thm)],[10988,30,theory(equality)]) ).
cnf(11060,negated_conjecture,
( product(esk1_0,product(esk2_0,esk1_0)) = esk1_0
| $false ),
inference(rw,[status(thm)],[11059,7551,theory(equality)]) ).
cnf(11061,negated_conjecture,
product(esk1_0,product(esk2_0,esk1_0)) = esk1_0,
inference(cn,[status(thm)],[11060,theory(equality)]) ).
cnf(11062,negated_conjecture,
$false,
inference(sr,[status(thm)],[11061,7555,theory(equality)]) ).
cnf(11063,negated_conjecture,
$false,
11062,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRP/GRP775+1.p
% --creating new selector for []
% -running prover on /tmp/tmpavXKju/sel_GRP775+1.p_1 with time limit 29
% -prover status Theorem
% Problem GRP775+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRP/GRP775+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRP/GRP775+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
%
%------------------------------------------------------------------------------