%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GRP655+2 : 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 11:20:13 EST 2010
% Result : Theorem 17.74s
% Output : CNFRefutation 17.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 6
% Syntax : Number of formulae : 171 ( 164 unt; 0 def)
% Number of atoms : 178 ( 174 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 11 ~; 5 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 354 ( 0 sgn 26 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] : mult(X3,mult(X2,mult(X1,X2))) = mult(mult(mult(X3,X2),X1),X2),
file('/tmp/tmpyRAK_o/sel_GRP655+2.p_1',f05) ).
fof(2,axiom,
! [X2,X3] : rd(mult(X3,X2),X2) = X3,
file('/tmp/tmpyRAK_o/sel_GRP655+2.p_1',f04) ).
fof(3,axiom,
! [X2,X3] : mult(X3,ld(X3,X2)) = X2,
file('/tmp/tmpyRAK_o/sel_GRP655+2.p_1',f01) ).
fof(4,conjecture,
! [X4,X5] :
( mult(X4,rd(X5,X5)) = X4
& mult(rd(X5,X5),X4) = X4 ),
file('/tmp/tmpyRAK_o/sel_GRP655+2.p_1',goals) ).
fof(5,axiom,
! [X2,X3] : mult(rd(X3,X2),X2) = X3,
file('/tmp/tmpyRAK_o/sel_GRP655+2.p_1',f03) ).
fof(6,axiom,
! [X2,X3] : ld(X3,mult(X3,X2)) = X2,
file('/tmp/tmpyRAK_o/sel_GRP655+2.p_1',f02) ).
fof(7,negated_conjecture,
~ ! [X4,X5] :
( mult(X4,rd(X5,X5)) = X4
& mult(rd(X5,X5),X4) = X4 ),
inference(assume_negation,[status(cth)],[4]) ).
fof(8,plain,
! [X4,X5,X6] : mult(X6,mult(X5,mult(X4,X5))) = mult(mult(mult(X6,X5),X4),X5),
inference(variable_rename,[status(thm)],[1]) ).
cnf(9,plain,
mult(X1,mult(X2,mult(X3,X2))) = mult(mult(mult(X1,X2),X3),X2),
inference(split_conjunct,[status(thm)],[8]) ).
fof(10,plain,
! [X4,X5] : rd(mult(X5,X4),X4) = X5,
inference(variable_rename,[status(thm)],[2]) ).
cnf(11,plain,
rd(mult(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[10]) ).
fof(12,plain,
! [X4,X5] : mult(X5,ld(X5,X4)) = X4,
inference(variable_rename,[status(thm)],[3]) ).
cnf(13,plain,
mult(X1,ld(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[12]) ).
fof(14,negated_conjecture,
? [X4,X5] :
( mult(X4,rd(X5,X5)) != X4
| mult(rd(X5,X5),X4) != X4 ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(15,negated_conjecture,
? [X6,X7] :
( mult(X6,rd(X7,X7)) != X6
| mult(rd(X7,X7),X6) != X6 ),
inference(variable_rename,[status(thm)],[14]) ).
fof(16,negated_conjecture,
( mult(esk1_0,rd(esk2_0,esk2_0)) != esk1_0
| mult(rd(esk2_0,esk2_0),esk1_0) != esk1_0 ),
inference(skolemize,[status(esa)],[15]) ).
cnf(17,negated_conjecture,
( mult(rd(esk2_0,esk2_0),esk1_0) != esk1_0
| mult(esk1_0,rd(esk2_0,esk2_0)) != esk1_0 ),
inference(split_conjunct,[status(thm)],[16]) ).
fof(18,plain,
! [X4,X5] : mult(rd(X5,X4),X4) = X5,
inference(variable_rename,[status(thm)],[5]) ).
cnf(19,plain,
mult(rd(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[18]) ).
fof(20,plain,
! [X4,X5] : ld(X5,mult(X5,X4)) = X4,
inference(variable_rename,[status(thm)],[6]) ).
cnf(21,plain,
ld(X1,mult(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[20]) ).
cnf(22,plain,
rd(X2,ld(X1,X2)) = X1,
inference(spm,[status(thm)],[11,13,theory(equality)]) ).
cnf(23,plain,
ld(rd(X1,X2),X1) = X2,
inference(spm,[status(thm)],[21,19,theory(equality)]) ).
cnf(24,plain,
mult(mult(X1,X3),X2) = mult(rd(X1,X2),mult(X2,mult(X3,X2))),
inference(spm,[status(thm)],[9,19,theory(equality)]) ).
cnf(25,plain,
rd(mult(X1,mult(X2,mult(X3,X2))),X2) = mult(mult(X1,X2),X3),
inference(spm,[status(thm)],[11,9,theory(equality)]) ).
cnf(39,plain,
mult(rd(X1,X2),mult(X2,X3)) = mult(mult(X1,rd(X3,X2)),X2),
inference(spm,[status(thm)],[24,19,theory(equality)]) ).
cnf(40,plain,
rd(mult(mult(X1,X3),X2),mult(X2,mult(X3,X2))) = rd(X1,X2),
inference(spm,[status(thm)],[11,24,theory(equality)]) ).
cnf(64,plain,
rd(mult(X1,mult(X2,X3)),X2) = mult(mult(X1,X2),rd(X3,X2)),
inference(spm,[status(thm)],[25,19,theory(equality)]) ).
cnf(81,plain,
rd(X1,X2) = mult(mult(rd(X1,mult(X2,X3)),X2),rd(X3,X2)),
inference(spm,[status(thm)],[64,19,theory(equality)]) ).
cnf(82,plain,
rd(mult(X1,X3),X2) = mult(mult(X1,X2),rd(ld(X2,X3),X2)),
inference(spm,[status(thm)],[64,13,theory(equality)]) ).
cnf(98,plain,
rd(mult(X1,X3),mult(X3,mult(X2,X3))) = rd(rd(X1,X2),X3),
inference(spm,[status(thm)],[40,19,theory(equality)]) ).
cnf(120,plain,
rd(X1,mult(X2,mult(X3,X2))) = rd(rd(rd(X1,X2),X3),X2),
inference(spm,[status(thm)],[98,19,theory(equality)]) ).
cnf(121,plain,
rd(mult(X1,X2),mult(X2,X3)) = rd(rd(X1,rd(X3,X2)),X2),
inference(spm,[status(thm)],[98,19,theory(equality)]) ).
cnf(126,plain,
ld(rd(rd(X1,X3),X2),mult(X1,X2)) = mult(X2,mult(X3,X2)),
inference(spm,[status(thm)],[23,98,theory(equality)]) ).
cnf(135,plain,
mult(rd(X1,mult(X2,mult(X3,X2))),X2) = rd(rd(X1,X2),X3),
inference(spm,[status(thm)],[19,120,theory(equality)]) ).
cnf(194,plain,
mult(rd(mult(X1,X3),mult(X3,X2)),X3) = rd(X1,rd(X2,X3)),
inference(spm,[status(thm)],[19,121,theory(equality)]) ).
cnf(215,plain,
mult(rd(X1,mult(X2,X3)),X2) = rd(rd(X1,X2),rd(X3,X2)),
inference(spm,[status(thm)],[135,19,theory(equality)]) ).
cnf(248,plain,
ld(mult(rd(X1,mult(X2,X3)),X2),rd(X1,X2)) = rd(X3,X2),
inference(spm,[status(thm)],[23,215,theory(equality)]) ).
cnf(275,plain,
mult(rd(mult(X1,X2),X3),X2) = rd(X1,rd(ld(X2,X3),X2)),
inference(spm,[status(thm)],[194,13,theory(equality)]) ).
cnf(542,plain,
mult(X1,rd(ld(X2,X3),X2)) = rd(mult(rd(X1,X2),X3),X2),
inference(spm,[status(thm)],[82,19,theory(equality)]) ).
cnf(603,plain,
rd(X1,X2) = mult(X1,rd(ld(X2,X2),X2)),
inference(spm,[status(thm)],[542,19,theory(equality)]) ).
cnf(631,plain,
mult(mult(rd(X1,mult(X2,mult(rd(X3,X2),X4))),X2),mult(X3,rd(ld(X2,X4),X2))) = rd(X1,X2),
inference(spm,[status(thm)],[81,542,theory(equality)]) ).
cnf(648,plain,
ld(X1,rd(X1,X2)) = rd(ld(X2,X2),X2),
inference(spm,[status(thm)],[21,603,theory(equality)]) ).
cnf(723,plain,
mult(ld(X2,rd(X2,X1)),X1) = ld(X1,X1),
inference(spm,[status(thm)],[19,648,theory(equality)]) ).
cnf(744,plain,
mult(mult(rd(X1,mult(X2,ld(X2,X2))),X2),ld(X3,rd(X3,X2))) = rd(X1,X2),
inference(spm,[status(thm)],[81,648,theory(equality)]) ).
cnf(746,plain,
rd(X1,ld(X3,rd(X3,X2))) = mult(rd(mult(X1,X2),X2),X2),
inference(spm,[status(thm)],[275,648,theory(equality)]) ).
cnf(764,plain,
mult(X1,ld(X3,rd(X3,X2))) = rd(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[744,13,theory(equality)]),19,theory(equality)]) ).
cnf(765,plain,
rd(X1,ld(X3,rd(X3,X2))) = mult(X1,X2),
inference(rw,[status(thm)],[746,11,theory(equality)]) ).
cnf(841,plain,
mult(X1,ld(X2,X3)) = rd(X1,ld(X3,X2)),
inference(spm,[status(thm)],[764,22,theory(equality)]) ).
cnf(1163,plain,
rd(mult(X1,ld(X3,X3)),ld(X2,rd(X2,X3))) = mult(mult(X1,ld(X2,rd(X2,X3))),rd(X3,ld(X2,rd(X2,X3)))),
inference(spm,[status(thm)],[64,723,theory(equality)]) ).
cnf(1201,plain,
mult(mult(X1,ld(X3,X3)),X3) = mult(mult(X1,ld(X2,rd(X2,X3))),rd(X3,ld(X2,rd(X2,X3)))),
inference(rw,[status(thm)],[1163,765,theory(equality)]) ).
cnf(1202,plain,
mult(mult(X1,ld(X3,X3)),X3) = mult(rd(X1,X3),mult(X3,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1201,764,theory(equality)]),765,theory(equality)]) ).
cnf(1277,plain,
mult(mult(X1,ld(X3,X2)),ld(X2,X3)) = X1,
inference(spm,[status(thm)],[19,841,theory(equality)]) ).
cnf(1680,plain,
mult(X1,X1) = mult(rd(X1,X1),mult(X1,X1)),
inference(spm,[status(thm)],[1202,13,theory(equality)]) ).
cnf(1747,plain,
rd(mult(X1,X1),mult(X1,X1)) = rd(X1,X1),
inference(spm,[status(thm)],[11,1680,theory(equality)]) ).
cnf(1752,plain,
rd(mult(X1,X1),X1) = mult(mult(rd(X1,X1),X1),rd(X1,X1)),
inference(spm,[status(thm)],[64,1680,theory(equality)]) ).
cnf(1776,plain,
X1 = mult(mult(rd(X1,X1),X1),rd(X1,X1)),
inference(rw,[status(thm)],[1752,11,theory(equality)]) ).
cnf(1777,plain,
X1 = mult(X1,rd(X1,X1)),
inference(rw,[status(thm)],[1776,19,theory(equality)]) ).
cnf(1785,plain,
ld(X1,X1) = rd(X1,X1),
inference(spm,[status(thm)],[21,1777,theory(equality)]) ).
cnf(1786,plain,
mult(mult(X1,X2),rd(X1,X1)) = mult(X1,mult(rd(X1,X1),mult(X2,rd(X1,X1)))),
inference(spm,[status(thm)],[9,1777,theory(equality)]) ).
cnf(1787,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,mult(rd(mult(X1,X2),mult(X1,X2)),X2))),
inference(spm,[status(thm)],[9,1777,theory(equality)]) ).
cnf(1788,plain,
mult(rd(X1,rd(X2,X2)),mult(rd(X2,X2),X2)) = mult(mult(X1,X2),rd(X2,X2)),
inference(spm,[status(thm)],[24,1777,theory(equality)]) ).
cnf(1791,plain,
rd(X1,mult(rd(X1,X1),mult(X2,rd(X1,X1)))) = rd(rd(X1,X2),rd(X1,X1)),
inference(spm,[status(thm)],[98,1777,theory(equality)]) ).
cnf(1792,plain,
rd(mult(X1,rd(X2,X2)),mult(rd(X2,X2),X2)) = rd(rd(X1,X2),rd(X2,X2)),
inference(spm,[status(thm)],[98,1777,theory(equality)]) ).
cnf(1794,plain,
mult(rd(X1,mult(rd(X2,X2),X2)),rd(X2,X2)) = rd(rd(X1,rd(X2,X2)),X2),
inference(spm,[status(thm)],[135,1777,theory(equality)]) ).
cnf(1795,plain,
mult(rd(X1,X2),mult(rd(X1,mult(X2,X1)),X2)) = rd(X1,X2),
inference(spm,[status(thm)],[1777,215,theory(equality)]) ).
cnf(1797,plain,
mult(rd(mult(X1,X2),X2),X2) = rd(X1,rd(rd(X2,X2),X2)),
inference(spm,[status(thm)],[194,1777,theory(equality)]) ).
cnf(1798,plain,
mult(mult(rd(X1,X2),X2),rd(rd(X2,X2),X2)) = rd(X1,X2),
inference(spm,[status(thm)],[81,1777,theory(equality)]) ).
cnf(1814,plain,
mult(rd(X1,rd(X2,X2)),X2) = mult(mult(X1,X2),rd(X2,X2)),
inference(rw,[status(thm)],[1788,19,theory(equality)]) ).
cnf(1817,plain,
rd(mult(X1,rd(X2,X2)),X2) = rd(rd(X1,X2),rd(X2,X2)),
inference(rw,[status(thm)],[1792,19,theory(equality)]) ).
cnf(1818,plain,
rd(mult(X1,rd(X2,X2)),X2) = mult(rd(X1,mult(X2,X2)),X2),
inference(rw,[status(thm)],[1817,215,theory(equality)]) ).
cnf(1819,plain,
mult(rd(X1,X2),rd(X2,X2)) = rd(rd(X1,rd(X2,X2)),X2),
inference(rw,[status(thm)],[1794,19,theory(equality)]) ).
cnf(1820,plain,
mult(rd(X1,X2),rd(X2,X2)) = rd(mult(X1,X2),mult(X2,X2)),
inference(rw,[status(thm)],[1819,121,theory(equality)]) ).
cnf(1821,plain,
mult(X1,X2) = rd(X1,rd(rd(X2,X2),X2)),
inference(rw,[status(thm)],[1797,11,theory(equality)]) ).
cnf(1822,plain,
mult(X1,rd(rd(X2,X2),X2)) = rd(X1,X2),
inference(rw,[status(thm)],[1798,19,theory(equality)]) ).
cnf(1970,plain,
rd(X1,rd(X2,X2)) = mult(X1,ld(X2,X2)),
inference(spm,[status(thm)],[841,1785,theory(equality)]) ).
cnf(1973,plain,
mult(mult(X1,rd(X2,X2)),ld(X2,X2)) = X1,
inference(spm,[status(thm)],[1277,1785,theory(equality)]) ).
cnf(1982,plain,
ld(X1,rd(X1,X2)) = rd(rd(X2,X2),X2),
inference(rw,[status(thm)],[648,1785,theory(equality)]) ).
cnf(1986,plain,
rd(X1,rd(X2,X2)) = mult(X1,rd(X2,X2)),
inference(rw,[status(thm)],[1970,1785,theory(equality)]) ).
cnf(1990,plain,
mult(mult(X1,rd(X2,X2)),rd(X2,X2)) = X1,
inference(rw,[status(thm)],[1973,1785,theory(equality)]) ).
cnf(2003,plain,
rd(mult(X1,rd(X2,X2)),X2) = rd(mult(X1,X2),mult(X2,X2)),
inference(spm,[status(thm)],[121,1986,theory(equality)]) ).
cnf(2062,plain,
mult(mult(X1,X1),rd(X1,X1)) = mult(X1,X1),
inference(spm,[status(thm)],[1777,1747,theory(equality)]) ).
cnf(2377,plain,
mult(mult(X1,X1),X1) = mult(X1,mult(X1,mult(rd(X1,X1),X1))),
inference(spm,[status(thm)],[9,2062,theory(equality)]) ).
cnf(2411,plain,
mult(mult(X1,X1),X1) = mult(X1,mult(X1,X1)),
inference(rw,[status(thm)],[2377,19,theory(equality)]) ).
cnf(3558,plain,
mult(rd(X1,X2),mult(X2,X2)) = mult(mult(X1,X2),rd(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1814,1986,theory(equality)]),39,theory(equality)]) ).
cnf(3559,plain,
rd(mult(mult(X1,X2),rd(X2,X2)),mult(X2,X2)) = rd(X1,X2),
inference(spm,[status(thm)],[11,3558,theory(equality)]) ).
cnf(3560,plain,
mult(X1,mult(X2,X2)) = mult(mult(mult(X1,X2),X2),rd(X2,X2)),
inference(spm,[status(thm)],[3558,11,theory(equality)]) ).
cnf(3655,plain,
rd(X1,X1) = mult(rd(X1,mult(X1,X1)),X1),
inference(spm,[status(thm)],[1818,1777,theory(equality)]) ).
cnf(3706,plain,
rd(rd(X1,X1),X1) = rd(X1,mult(X1,X1)),
inference(spm,[status(thm)],[11,3655,theory(equality)]) ).
cnf(3721,plain,
mult(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(spm,[status(thm)],[81,3655,theory(equality)]) ).
cnf(4036,plain,
rd(rd(X1,mult(X1,X1)),X1) = rd(X1,mult(X1,mult(X1,X1))),
inference(spm,[status(thm)],[120,3706,theory(equality)]) ).
cnf(4068,plain,
mult(X1,rd(X2,mult(X2,X2))) = rd(X1,X2),
inference(rw,[status(thm)],[1822,3706,theory(equality)]) ).
cnf(4069,plain,
rd(X1,rd(X2,mult(X2,X2))) = mult(X1,X2),
inference(rw,[status(thm)],[1821,3706,theory(equality)]) ).
cnf(4070,plain,
ld(X1,rd(X1,X2)) = rd(X2,mult(X2,X2)),
inference(rw,[status(thm)],[1982,3706,theory(equality)]) ).
cnf(4212,plain,
rd(mult(rd(X1,mult(mult(X2,X2),X2)),mult(X2,X2)),X2) = rd(X1,mult(X2,X2)),
inference(spm,[status(thm)],[81,4068,theory(equality)]) ).
cnf(4273,plain,
mult(rd(rd(X1,X2),X2),rd(X2,X2)) = rd(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[4212,2411,theory(equality)]),64,theory(equality)]),135,theory(equality)]) ).
cnf(5454,plain,
mult(rd(X1,mult(X2,X2)),X2) = rd(mult(X1,X2),mult(X2,X2)),
inference(rw,[status(thm)],[2003,1818,theory(equality)]) ).
cnf(5455,plain,
mult(rd(X1,mult(X2,X2)),X2) = mult(rd(X1,X2),rd(X2,X2)),
inference(rw,[status(thm)],[5454,1820,theory(equality)]) ).
cnf(8891,plain,
rd(rd(X1,mult(X2,X2)),rd(X2,X2)) = rd(rd(X1,X2),X2),
inference(spm,[status(thm)],[11,4273,theory(equality)]) ).
cnf(8945,plain,
mult(rd(rd(X1,rd(X2,mult(X2,X2))),rd(X2,mult(X2,X2))),mult(rd(X2,mult(X2,X2)),X2)) = rd(X1,mult(rd(X2,mult(X2,X2)),rd(X2,mult(X2,X2)))),
inference(spm,[status(thm)],[4273,4069,theory(equality)]) ).
cnf(8980,plain,
mult(rd(X1,mult(X2,X2)),rd(X2,X2)) = rd(rd(X1,X2),X2),
inference(rw,[status(thm)],[8891,1986,theory(equality)]) ).
cnf(9023,plain,
mult(X1,mult(X2,X2)) = rd(X1,mult(rd(X2,mult(X2,X2)),rd(X2,mult(X2,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[8945,4069,theory(equality)]),4069,theory(equality)]),3655,theory(equality)]),3560,theory(equality)]) ).
cnf(9024,plain,
mult(X1,mult(X2,X2)) = rd(X1,rd(X2,mult(X2,mult(X2,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[9023,4068,theory(equality)]),4036,theory(equality)]) ).
cnf(12770,plain,
mult(rd(rd(X1,X1),mult(X1,X1)),mult(rd(rd(X1,X1),mult(X1,X1)),mult(X1,X1))) = rd(rd(X1,X1),mult(X1,X1)),
inference(spm,[status(thm)],[1795,2062,theory(equality)]) ).
cnf(12898,plain,
rd(X1,mult(X1,mult(X1,X1))) = rd(rd(X1,X1),mult(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[12770,19,theory(equality)]),8980,theory(equality)]),120,theory(equality)]) ).
cnf(13485,plain,
rd(rd(X1,X2),mult(X2,X2)) = rd(rd(X1,mult(X2,X2)),X2),
inference(spm,[status(thm)],[3559,81,theory(equality)]) ).
cnf(15301,plain,
ld(rd(rd(X1,mult(rd(X2,mult(X2,X2)),X3)),X2),rd(X1,rd(X2,mult(X2,X2)))) = rd(X3,rd(X2,mult(X2,X2))),
inference(spm,[status(thm)],[248,4068,theory(equality)]) ).
cnf(15396,plain,
mult(X2,mult(mult(rd(X2,mult(X2,X2)),X3),X2)) = rd(X3,rd(X2,mult(X2,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[15301,4069,theory(equality)]),126,theory(equality)]) ).
cnf(15397,plain,
mult(X2,mult(mult(rd(X2,mult(X2,X2)),X3),X2)) = mult(X3,X2),
inference(rw,[status(thm)],[15396,4069,theory(equality)]) ).
cnf(15721,plain,
ld(X1,mult(X2,X1)) = mult(mult(rd(X1,mult(X1,X1)),X2),X1),
inference(spm,[status(thm)],[21,15397,theory(equality)]) ).
cnf(15780,plain,
mult(rd(X1,mult(X1,X1)),mult(mult(rd(rd(X1,mult(X1,X1)),rd(rd(X1,mult(X1,X1)),X1)),X2),rd(X1,mult(X1,X1)))) = mult(X2,rd(X1,mult(X1,X1))),
inference(spm,[status(thm)],[15397,4068,theory(equality)]) ).
cnf(15900,plain,
mult(rd(X1,mult(X1,X1)),rd(mult(X1,X2),X1)) = mult(X2,rd(X1,mult(X1,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[15780,13485,theory(equality)]),12898,theory(equality)]),9024,theory(equality)]),19,theory(equality)]),4068,theory(equality)]) ).
cnf(15901,plain,
mult(rd(X1,mult(X1,X1)),rd(mult(X1,X2),X1)) = rd(X2,X1),
inference(rw,[status(thm)],[15900,4068,theory(equality)]) ).
cnf(16074,plain,
rd(rd(X2,X1),rd(mult(X1,X2),X1)) = rd(X1,mult(X1,X1)),
inference(spm,[status(thm)],[11,15901,theory(equality)]) ).
cnf(16231,plain,
mult(rd(X2,mult(X1,mult(X1,X2))),X1) = rd(X1,mult(X1,X1)),
inference(rw,[status(thm)],[16074,215,theory(equality)]) ).
cnf(16352,plain,
rd(rd(X2,mult(X2,X2)),X2) = rd(X1,mult(X2,mult(X2,X1))),
inference(spm,[status(thm)],[11,16231,theory(equality)]) ).
cnf(16408,plain,
mult(rd(rd(X2,X2),mult(rd(X2,X2),rd(X2,X2))),rd(X2,X2)) = rd(X1,mult(rd(X2,X2),mult(rd(X2,X2),X1))),
inference(spm,[status(thm)],[1990,16231,theory(equality)]) ).
cnf(16462,plain,
mult(mult(rd(X2,mult(X2,X2)),X2),rd(X2,X2)) = mult(rd(X1,mult(X2,mult(X2,X1))),mult(X2,X2)),
inference(spm,[status(thm)],[3560,16231,theory(equality)]) ).
cnf(16522,plain,
rd(X2,mult(X2,mult(X2,X2))) = rd(X1,mult(X2,mult(X2,X1))),
inference(rw,[status(thm)],[16352,4036,theory(equality)]) ).
cnf(16547,plain,
rd(X2,X2) = rd(X1,mult(rd(X2,X2),mult(rd(X2,X2),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[16408,3721,theory(equality)]),215,theory(equality)]),3655,theory(equality)]),3721,theory(equality)]) ).
cnf(16577,plain,
rd(X2,X2) = mult(rd(X1,mult(X2,mult(X2,X1))),mult(X2,X2)),
inference(rw,[status(thm)],[16462,81,theory(equality)]) ).
cnf(17287,plain,
mult(mult(rd(rd(X1,X1),rd(X1,X1)),X2),rd(X1,X1)) = ld(rd(X1,X1),mult(X2,rd(X1,X1))),
inference(spm,[status(thm)],[15721,3721,theory(equality)]) ).
cnf(17385,plain,
mult(mult(ld(X3,rd(X3,X1)),X2),X1) = ld(X1,mult(X2,X1)),
inference(spm,[status(thm)],[15721,4070,theory(equality)]) ).
cnf(17432,plain,
mult(mult(rd(X1,X1),X2),rd(X1,X1)) = ld(rd(X1,X1),mult(X2,rd(X1,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[17287,215,theory(equality)]),5455,theory(equality)]),3721,theory(equality)]) ).
cnf(17708,plain,
ld(rd(X2,X2),X1) = mult(rd(X2,X2),mult(rd(X2,X2),X1)),
inference(spm,[status(thm)],[23,16547,theory(equality)]) ).
cnf(17858,plain,
mult(rd(X1,mult(X2,X2)),mult(mult(X2,X2),rd(X2,X2))) = mult(mult(X1,rd(X3,mult(X2,mult(X2,X3)))),mult(X2,X2)),
inference(spm,[status(thm)],[24,16577,theory(equality)]) ).
cnf(18001,plain,
X1 = mult(mult(X1,rd(X3,mult(X2,mult(X2,X3)))),mult(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[17858,2062,theory(equality)]),19,theory(equality)]) ).
cnf(21024,plain,
mult(X1,mult(X3,X3)) = rd(X1,rd(X2,mult(X3,mult(X3,X2)))),
inference(spm,[status(thm)],[18001,19,theory(equality)]) ).
cnf(21025,plain,
rd(X1,mult(X3,X3)) = mult(X1,rd(X2,mult(X3,mult(X3,X2)))),
inference(spm,[status(thm)],[11,18001,theory(equality)]) ).
cnf(23582,plain,
mult(rd(X2,mult(X2,mult(X2,X2))),mult(X2,mult(X2,X1))) = X1,
inference(spm,[status(thm)],[19,16522,theory(equality)]) ).
cnf(25317,plain,
mult(rd(X3,mult(X1,mult(X1,X3))),mult(X1,mult(X1,X2))) = X2,
inference(spm,[status(thm)],[23582,16522,theory(equality)]) ).
cnf(26650,plain,
ld(rd(X1,mult(X2,mult(X2,X1))),X3) = mult(X2,mult(X2,X3)),
inference(spm,[status(thm)],[21,25317,theory(equality)]) ).
cnf(56096,plain,
mult(mult(ld(X1,mult(X1,mult(X3,X3))),X4),rd(X2,mult(X3,mult(X3,X2)))) = ld(rd(X2,mult(X3,mult(X3,X2))),mult(X4,rd(X2,mult(X3,mult(X3,X2))))),
inference(spm,[status(thm)],[17385,21024,theory(equality)]) ).
cnf(56334,plain,
rd(mult(mult(X3,X3),X4),mult(X3,X3)) = ld(rd(X2,mult(X3,mult(X3,X2))),mult(X4,rd(X2,mult(X3,mult(X3,X2))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[56096,21,theory(equality)]),21025,theory(equality)]) ).
cnf(56335,plain,
rd(mult(mult(X3,X3),X4),mult(X3,X3)) = mult(X3,mult(X3,rd(X4,mult(X3,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[56334,21025,theory(equality)]),26650,theory(equality)]) ).
cnf(78623,plain,
mult(X1,mult(rd(X1,X1),X2)) = mult(mult(X1,rd(X2,rd(X1,X1))),rd(X1,X1)),
inference(spm,[status(thm)],[1786,19,theory(equality)]) ).
cnf(78889,plain,
mult(X1,mult(rd(X1,X1),X2)) = mult(mult(X1,mult(X2,rd(X1,X1))),rd(X1,X1)),
inference(rw,[status(thm)],[78623,1986,theory(equality)]) ).
cnf(79711,plain,
rd(X1,mult(rd(X1,X1),mult(X2,rd(X1,X1)))) = mult(rd(X1,X2),rd(X1,X1)),
inference(rw,[status(thm)],[1791,1986,theory(equality)]) ).
cnf(79715,plain,
ld(mult(rd(X1,X2),rd(X1,X1)),X1) = mult(rd(X1,X1),mult(X2,rd(X1,X1))),
inference(spm,[status(thm)],[23,79711,theory(equality)]) ).
cnf(232899,plain,
mult(X1,mult(rd(X2,mult(X2,X2)),mult(rd(rd(X1,X2),rd(X1,X2)),rd(X2,mult(X2,X2))))) = mult(rd(X1,X2),rd(X2,mult(X2,X2))),
inference(spm,[status(thm)],[1787,4068,theory(equality)]) ).
cnf(233578,plain,
mult(X1,mult(rd(X2,mult(X2,X2)),rd(X1,mult(X2,X1)))) = mult(rd(X1,X2),rd(X2,mult(X2,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[232899,215,theory(equality)]),4068,theory(equality)]),11,theory(equality)]) ).
cnf(233579,plain,
mult(X1,mult(rd(X2,mult(X2,X2)),rd(X1,mult(X2,X1)))) = rd(rd(X1,X2),X2),
inference(rw,[status(thm)],[233578,4068,theory(equality)]) ).
cnf(309633,plain,
mult(X1,mult(rd(rd(X2,X2),rd(X2,X2)),rd(X1,mult(rd(X2,X2),X1)))) = rd(rd(X1,rd(X2,X2)),rd(X2,X2)),
inference(spm,[status(thm)],[233579,3721,theory(equality)]) ).
cnf(310353,plain,
mult(X1,mult(rd(X2,X2),rd(X1,mult(rd(X2,X2),X1)))) = rd(rd(X1,rd(X2,X2)),rd(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[309633,215,theory(equality)]),3655,theory(equality)]) ).
cnf(310354,plain,
mult(X1,mult(rd(X2,X2),rd(X1,mult(rd(X2,X2),X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[310353,1986,theory(equality)]),11,theory(equality)]) ).
cnf(312484,plain,
ld(X1,X1) = mult(rd(X2,X2),rd(X1,mult(rd(X2,X2),X1))),
inference(spm,[status(thm)],[21,310354,theory(equality)]) ).
cnf(313056,plain,
rd(X1,X1) = mult(rd(X2,X2),rd(X1,mult(rd(X2,X2),X1))),
inference(rw,[status(thm)],[312484,1785,theory(equality)]) ).
cnf(313576,plain,
ld(rd(X1,X1),rd(X2,X2)) = rd(X2,mult(rd(X1,X1),X2)),
inference(spm,[status(thm)],[21,313056,theory(equality)]) ).
cnf(314447,plain,
ld(rd(X1,X1),mult(rd(X2,X2),rd(X2,X2))) = rd(mult(X2,X2),mult(rd(X1,X1),mult(X2,X2))),
inference(spm,[status(thm)],[313576,1820,theory(equality)]) ).
cnf(314639,plain,
rd(X2,mult(rd(X1,X1),X2)) = rd(mult(X2,X2),mult(rd(X1,X1),mult(X2,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[314447,3721,theory(equality)]),313576,theory(equality)]) ).
cnf(322625,plain,
mult(mult(rd(rd(X1,rd(X2,X2)),mult(rd(X2,X2),rd(X1,rd(X2,X2)))),rd(X2,X2)),mult(X1,rd(ld(rd(X2,X2),rd(X1,rd(X2,X2))),rd(X2,X2)))) = rd(mult(rd(X1,rd(X2,X2)),rd(X1,rd(X2,X2))),rd(X2,X2)),
inference(spm,[status(thm)],[631,314639,theory(equality)]) ).
cnf(322962,plain,
mult(mult(X1,rd(X2,X2)),X1) = rd(mult(rd(X1,rd(X2,X2)),rd(X1,rd(X2,X2))),rd(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[322625,1986,theory(equality)]),1986,theory(equality)]),98,theory(equality)]),1986,theory(equality)]),1990,theory(equality)]),1986,theory(equality)]),17432,theory(equality)]),11,theory(equality)]),24,theory(equality)]) ).
cnf(322963,plain,
mult(mult(X1,rd(X2,X2)),X1) = mult(X1,mult(rd(X2,X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[322962,1986,theory(equality)]),1986,theory(equality)]),1986,theory(equality)]),9,theory(equality)]),1990,theory(equality)]) ).
cnf(322973,plain,
rd(mult(X1,mult(rd(X2,X2),X1)),X1) = mult(X1,rd(X2,X2)),
inference(spm,[status(thm)],[11,322963,theory(equality)]) ).
cnf(324248,plain,
mult(mult(X1,X1),rd(X2,X2)) = mult(X1,mult(X1,rd(mult(rd(X2,X2),mult(X1,X1)),mult(X1,X1)))),
inference(spm,[status(thm)],[56335,322973,theory(equality)]) ).
cnf(324577,plain,
mult(mult(X1,X1),rd(X2,X2)) = mult(X1,mult(X1,rd(X2,X2))),
inference(rw,[status(thm)],[324248,11,theory(equality)]) ).
cnf(325468,plain,
mult(rd(X1,X1),rd(X2,X2)) = mult(rd(X1,X1),mult(rd(X1,X1),rd(X2,X2))),
inference(spm,[status(thm)],[324577,3721,theory(equality)]) ).
cnf(325986,plain,
mult(rd(X1,X1),rd(X2,X2)) = rd(X2,mult(rd(X1,X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[325468,17708,theory(equality)]),313576,theory(equality)]) ).
cnf(326867,plain,
mult(rd(X1,X1),mult(rd(X1,X1),rd(X2,X2))) = rd(X2,X2),
inference(rw,[status(thm)],[313056,325986,theory(equality)]) ).
cnf(326868,plain,
mult(rd(X1,X1),rd(X2,X2)) = rd(X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[326867,17708,theory(equality)]),313576,theory(equality)]),325986,theory(equality)]) ).
cnf(327652,plain,
mult(mult(X1,rd(X1,X1)),rd(X1,X1)) = mult(X1,mult(rd(X1,X1),rd(X2,X2))),
inference(spm,[status(thm)],[78889,326868,theory(equality)]) ).
cnf(328470,plain,
X1 = mult(X1,mult(rd(X1,X1),rd(X2,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[327652,1777,theory(equality)]),1777,theory(equality)]) ).
cnf(328471,plain,
X1 = mult(X1,rd(X2,X2)),
inference(rw,[status(thm)],[328470,326868,theory(equality)]) ).
cnf(329496,plain,
ld(rd(X1,X2),X1) = mult(rd(X1,X1),mult(X2,rd(X1,X1))),
inference(rw,[status(thm)],[79715,328471,theory(equality)]) ).
cnf(329497,plain,
ld(rd(X1,X2),X1) = mult(rd(X1,X1),X2),
inference(rw,[status(thm)],[329496,328471,theory(equality)]) ).
cnf(329498,plain,
X2 = mult(rd(X1,X1),X2),
inference(rw,[status(thm)],[329497,23,theory(equality)]) ).
cnf(329561,negated_conjecture,
( $false
| mult(rd(esk2_0,esk2_0),esk1_0) != esk1_0 ),
inference(rw,[status(thm)],[17,328471,theory(equality)]) ).
cnf(329562,negated_conjecture,
mult(rd(esk2_0,esk2_0),esk1_0) != esk1_0,
inference(cn,[status(thm)],[329561,theory(equality)]) ).
cnf(335016,negated_conjecture,
$false,
inference(rw,[status(thm)],[329562,329498,theory(equality)]) ).
cnf(335017,negated_conjecture,
$false,
inference(cn,[status(thm)],[335016,theory(equality)]) ).
cnf(335018,negated_conjecture,
$false,
335017,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRP/GRP655+2.p
% --creating new selector for []
% -running prover on /tmp/tmpyRAK_o/sel_GRP655+2.p_1 with time limit 29
% -prover status Theorem
% Problem GRP655+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRP/GRP655+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRP/GRP655+2.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
%
%------------------------------------------------------------------------------