TSTP Solution File: GRP194+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : GRP194+1 : TPTP v5.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 10:04:19 EST 2010
% Result : Theorem 0.22s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 12 unt; 0 def)
% Number of atoms : 139 ( 30 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 160 ( 68 ~; 65 |; 22 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 60 ( 0 sgn 32 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X2] :
( group_member(X2,h)
=> ? [X3] :
( group_member(X3,f)
& phi(X3) = X2 ) ),
file('/tmp/tmpvN4Lao/sel_GRP194+1.p_1',surjective) ).
fof(4,axiom,
! [X1,X2] :
( left_zero(X1,X2)
<=> ( group_member(X2,X1)
& ! [X3] :
( group_member(X3,X1)
=> multiply(X1,X2,X3) = X2 ) ) ),
file('/tmp/tmpvN4Lao/sel_GRP194+1.p_1',left_zero) ).
fof(5,axiom,
! [X2] :
( group_member(X2,f)
=> group_member(phi(X2),h) ),
file('/tmp/tmpvN4Lao/sel_GRP194+1.p_1',homomorphism1) ).
fof(6,axiom,
! [X2,X3] :
( ( group_member(X2,f)
& group_member(X3,f) )
=> multiply(h,phi(X2),phi(X3)) = phi(multiply(f,X2,X3)) ),
file('/tmp/tmpvN4Lao/sel_GRP194+1.p_1',homomorphism2) ).
fof(7,conjecture,
left_zero(h,phi(f_left_zero)),
file('/tmp/tmpvN4Lao/sel_GRP194+1.p_1',prove_left_zero_h) ).
fof(8,axiom,
left_zero(f,f_left_zero),
file('/tmp/tmpvN4Lao/sel_GRP194+1.p_1',left_zero_for_f) ).
fof(9,negated_conjecture,
~ left_zero(h,phi(f_left_zero)),
inference(assume_negation,[status(cth)],[7]) ).
fof(10,negated_conjecture,
~ left_zero(h,phi(f_left_zero)),
inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).
fof(17,plain,
! [X2] :
( ~ group_member(X2,h)
| ? [X3] :
( group_member(X3,f)
& phi(X3) = X2 ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(18,plain,
! [X4] :
( ~ group_member(X4,h)
| ? [X5] :
( group_member(X5,f)
& phi(X5) = X4 ) ),
inference(variable_rename,[status(thm)],[17]) ).
fof(19,plain,
! [X4] :
( ~ group_member(X4,h)
| ( group_member(esk1_1(X4),f)
& phi(esk1_1(X4)) = X4 ) ),
inference(skolemize,[status(esa)],[18]) ).
fof(20,plain,
! [X4] :
( ( group_member(esk1_1(X4),f)
| ~ group_member(X4,h) )
& ( phi(esk1_1(X4)) = X4
| ~ group_member(X4,h) ) ),
inference(distribute,[status(thm)],[19]) ).
cnf(21,plain,
( phi(esk1_1(X1)) = X1
| ~ group_member(X1,h) ),
inference(split_conjunct,[status(thm)],[20]) ).
cnf(22,plain,
( group_member(esk1_1(X1),f)
| ~ group_member(X1,h) ),
inference(split_conjunct,[status(thm)],[20]) ).
fof(23,plain,
! [X1,X2] :
( ( ~ left_zero(X1,X2)
| ( group_member(X2,X1)
& ! [X3] :
( ~ group_member(X3,X1)
| multiply(X1,X2,X3) = X2 ) ) )
& ( ~ group_member(X2,X1)
| ? [X3] :
( group_member(X3,X1)
& multiply(X1,X2,X3) != X2 )
| left_zero(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(24,plain,
! [X4,X5] :
( ( ~ left_zero(X4,X5)
| ( group_member(X5,X4)
& ! [X6] :
( ~ group_member(X6,X4)
| multiply(X4,X5,X6) = X5 ) ) )
& ( ~ group_member(X5,X4)
| ? [X7] :
( group_member(X7,X4)
& multiply(X4,X5,X7) != X5 )
| left_zero(X4,X5) ) ),
inference(variable_rename,[status(thm)],[23]) ).
fof(25,plain,
! [X4,X5] :
( ( ~ left_zero(X4,X5)
| ( group_member(X5,X4)
& ! [X6] :
( ~ group_member(X6,X4)
| multiply(X4,X5,X6) = X5 ) ) )
& ( ~ group_member(X5,X4)
| ( group_member(esk2_2(X4,X5),X4)
& multiply(X4,X5,esk2_2(X4,X5)) != X5 )
| left_zero(X4,X5) ) ),
inference(skolemize,[status(esa)],[24]) ).
fof(26,plain,
! [X4,X5,X6] :
( ( ( ( ~ group_member(X6,X4)
| multiply(X4,X5,X6) = X5 )
& group_member(X5,X4) )
| ~ left_zero(X4,X5) )
& ( ~ group_member(X5,X4)
| ( group_member(esk2_2(X4,X5),X4)
& multiply(X4,X5,esk2_2(X4,X5)) != X5 )
| left_zero(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[25]) ).
fof(27,plain,
! [X4,X5,X6] :
( ( ~ group_member(X6,X4)
| multiply(X4,X5,X6) = X5
| ~ left_zero(X4,X5) )
& ( group_member(X5,X4)
| ~ left_zero(X4,X5) )
& ( group_member(esk2_2(X4,X5),X4)
| ~ group_member(X5,X4)
| left_zero(X4,X5) )
& ( multiply(X4,X5,esk2_2(X4,X5)) != X5
| ~ group_member(X5,X4)
| left_zero(X4,X5) ) ),
inference(distribute,[status(thm)],[26]) ).
cnf(28,plain,
( left_zero(X1,X2)
| ~ group_member(X2,X1)
| multiply(X1,X2,esk2_2(X1,X2)) != X2 ),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(29,plain,
( left_zero(X1,X2)
| group_member(esk2_2(X1,X2),X1)
| ~ group_member(X2,X1) ),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(30,plain,
( group_member(X2,X1)
| ~ left_zero(X1,X2) ),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(31,plain,
( multiply(X1,X2,X3) = X2
| ~ left_zero(X1,X2)
| ~ group_member(X3,X1) ),
inference(split_conjunct,[status(thm)],[27]) ).
fof(32,plain,
! [X2] :
( ~ group_member(X2,f)
| group_member(phi(X2),h) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(33,plain,
! [X3] :
( ~ group_member(X3,f)
| group_member(phi(X3),h) ),
inference(variable_rename,[status(thm)],[32]) ).
cnf(34,plain,
( group_member(phi(X1),h)
| ~ group_member(X1,f) ),
inference(split_conjunct,[status(thm)],[33]) ).
fof(35,plain,
! [X2,X3] :
( ~ group_member(X2,f)
| ~ group_member(X3,f)
| multiply(h,phi(X2),phi(X3)) = phi(multiply(f,X2,X3)) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(36,plain,
! [X4,X5] :
( ~ group_member(X4,f)
| ~ group_member(X5,f)
| multiply(h,phi(X4),phi(X5)) = phi(multiply(f,X4,X5)) ),
inference(variable_rename,[status(thm)],[35]) ).
cnf(37,plain,
( multiply(h,phi(X1),phi(X2)) = phi(multiply(f,X1,X2))
| ~ group_member(X2,f)
| ~ group_member(X1,f) ),
inference(split_conjunct,[status(thm)],[36]) ).
cnf(38,negated_conjecture,
~ left_zero(h,phi(f_left_zero)),
inference(split_conjunct,[status(thm)],[10]) ).
cnf(39,plain,
left_zero(f,f_left_zero),
inference(split_conjunct,[status(thm)],[8]) ).
cnf(40,plain,
group_member(f_left_zero,f),
inference(spm,[status(thm)],[30,39,theory(equality)]) ).
cnf(42,plain,
( multiply(f,f_left_zero,X1) = f_left_zero
| ~ group_member(X1,f) ),
inference(spm,[status(thm)],[31,39,theory(equality)]) ).
cnf(44,plain,
( multiply(h,phi(X1),X2) = phi(multiply(f,X1,esk1_1(X2)))
| ~ group_member(esk1_1(X2),f)
| ~ group_member(X1,f)
| ~ group_member(X2,h) ),
inference(spm,[status(thm)],[37,21,theory(equality)]) ).
cnf(164,plain,
( phi(multiply(f,X1,esk1_1(X2))) = multiply(h,phi(X1),X2)
| ~ group_member(X1,f)
| ~ group_member(X2,h) ),
inference(csr,[status(thm)],[44,22]) ).
cnf(169,plain,
( phi(f_left_zero) = multiply(h,phi(f_left_zero),X1)
| ~ group_member(f_left_zero,f)
| ~ group_member(X1,h)
| ~ group_member(esk1_1(X1),f) ),
inference(spm,[status(thm)],[164,42,theory(equality)]) ).
cnf(171,plain,
( phi(f_left_zero) = multiply(h,phi(f_left_zero),X1)
| $false
| ~ group_member(X1,h)
| ~ group_member(esk1_1(X1),f) ),
inference(rw,[status(thm)],[169,40,theory(equality)]) ).
cnf(172,plain,
( phi(f_left_zero) = multiply(h,phi(f_left_zero),X1)
| ~ group_member(X1,h)
| ~ group_member(esk1_1(X1),f) ),
inference(cn,[status(thm)],[171,theory(equality)]) ).
cnf(173,plain,
( multiply(h,phi(f_left_zero),X1) = phi(f_left_zero)
| ~ group_member(X1,h) ),
inference(csr,[status(thm)],[172,22]) ).
cnf(174,plain,
( left_zero(h,phi(f_left_zero))
| ~ group_member(phi(f_left_zero),h)
| ~ group_member(esk2_2(h,phi(f_left_zero)),h) ),
inference(spm,[status(thm)],[28,173,theory(equality)]) ).
cnf(178,plain,
( ~ group_member(phi(f_left_zero),h)
| ~ group_member(esk2_2(h,phi(f_left_zero)),h) ),
inference(sr,[status(thm)],[174,38,theory(equality)]) ).
cnf(181,plain,
( left_zero(h,phi(f_left_zero))
| ~ group_member(phi(f_left_zero),h) ),
inference(spm,[status(thm)],[178,29,theory(equality)]) ).
cnf(182,plain,
~ group_member(phi(f_left_zero),h),
inference(sr,[status(thm)],[181,38,theory(equality)]) ).
cnf(183,plain,
~ group_member(f_left_zero,f),
inference(spm,[status(thm)],[182,34,theory(equality)]) ).
cnf(184,plain,
$false,
inference(rw,[status(thm)],[183,40,theory(equality)]) ).
cnf(185,plain,
$false,
inference(cn,[status(thm)],[184,theory(equality)]) ).
cnf(186,plain,
$false,
185,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRP/GRP194+1.p
% --creating new selector for [GRP007+0.ax]
% -running prover on /tmp/tmpvN4Lao/sel_GRP194+1.p_1 with time limit 29
% -prover status Theorem
% Problem GRP194+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRP/GRP194+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRP/GRP194+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
%
%------------------------------------------------------------------------------