TSTP Solution File: HAL006+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : HAL006+1 : TPTP v5.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art02.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 11:36:26 EST 2010
% Result : Theorem 1.20s
% Output : CNFRefutation 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 7 unt; 0 def)
% Number of atoms : 173 ( 47 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 212 ( 88 ~; 76 |; 40 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-3 aty)
% Number of variables : 111 ( 0 sgn 64 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(5,axiom,
! [X2,X4,X5] :
( ( element(X4,X2)
& element(X5,X2) )
=> subtract(X2,X4,subtract(X2,X4,X5)) = X5 ),
file('/tmp/tmp5H0de9/sel_HAL006+1.p_1',subtract_cancellation) ).
fof(7,axiom,
! [X1,X2,X3] :
( morphism(X1,X2,X3)
=> ! [X4,X5] :
( ( element(X4,X2)
& element(X5,X2) )
=> apply(X1,subtract(X2,X4,X5)) = subtract(X3,apply(X1,X4),apply(X1,X5)) ) ),
file('/tmp/tmp5H0de9/sel_HAL006+1.p_1',subtract_distribution) ).
fof(13,axiom,
! [X1,X2,X3] :
( morphism(X1,X2,X3)
=> ( ! [X17] :
( element(X17,X2)
=> element(apply(X1,X17),X3) )
& apply(X1,zero(X2)) = zero(X3) ) ),
file('/tmp/tmp5H0de9/sel_HAL006+1.p_1',morphism) ).
fof(16,axiom,
! [X19] :
( element(X19,e)
=> ? [X20,X21,X22] :
( element(X20,b)
& element(X21,e)
& subtract(e,apply(g,X20),X19) = X21
& element(X22,a)
& apply(gamma,apply(f,X22)) = X21
& apply(g,apply(alpha,X22)) = X21 ) ),
file('/tmp/tmp5H0de9/sel_HAL006+1.p_1',lemma8) ).
fof(20,axiom,
morphism(g,b,e),
file('/tmp/tmp5H0de9/sel_HAL006+1.p_1',g_morphism) ).
fof(22,axiom,
morphism(alpha,a,b),
file('/tmp/tmp5H0de9/sel_HAL006+1.p_1',alpha_morphism) ).
fof(24,conjecture,
! [X19] :
( element(X19,e)
=> ? [X20,X24] :
( element(X20,b)
& element(X24,b)
& apply(g,subtract(b,X20,X24)) = X19 ) ),
file('/tmp/tmp5H0de9/sel_HAL006+1.p_1',lemma12) ).
fof(34,negated_conjecture,
~ ! [X19] :
( element(X19,e)
=> ? [X20,X24] :
( element(X20,b)
& element(X24,b)
& apply(g,subtract(b,X20,X24)) = X19 ) ),
inference(assume_negation,[status(cth)],[24]) ).
fof(58,plain,
! [X2,X4,X5] :
( ~ element(X4,X2)
| ~ element(X5,X2)
| subtract(X2,X4,subtract(X2,X4,X5)) = X5 ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(59,plain,
! [X6,X7,X8] :
( ~ element(X7,X6)
| ~ element(X8,X6)
| subtract(X6,X7,subtract(X6,X7,X8)) = X8 ),
inference(variable_rename,[status(thm)],[58]) ).
cnf(60,plain,
( subtract(X1,X2,subtract(X1,X2,X3)) = X3
| ~ element(X3,X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[59]) ).
fof(69,plain,
! [X1,X2,X3] :
( ~ morphism(X1,X2,X3)
| ! [X4,X5] :
( ~ element(X4,X2)
| ~ element(X5,X2)
| apply(X1,subtract(X2,X4,X5)) = subtract(X3,apply(X1,X4),apply(X1,X5)) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(70,plain,
! [X6,X7,X8] :
( ~ morphism(X6,X7,X8)
| ! [X9,X10] :
( ~ element(X9,X7)
| ~ element(X10,X7)
| apply(X6,subtract(X7,X9,X10)) = subtract(X8,apply(X6,X9),apply(X6,X10)) ) ),
inference(variable_rename,[status(thm)],[69]) ).
fof(71,plain,
! [X6,X7,X8,X9,X10] :
( ~ element(X9,X7)
| ~ element(X10,X7)
| apply(X6,subtract(X7,X9,X10)) = subtract(X8,apply(X6,X9),apply(X6,X10))
| ~ morphism(X6,X7,X8) ),
inference(shift_quantors,[status(thm)],[70]) ).
cnf(72,plain,
( apply(X1,subtract(X2,X4,X5)) = subtract(X3,apply(X1,X4),apply(X1,X5))
| ~ morphism(X1,X2,X3)
| ~ element(X5,X2)
| ~ element(X4,X2) ),
inference(split_conjunct,[status(thm)],[71]) ).
fof(103,plain,
! [X1,X2,X3] :
( ~ morphism(X1,X2,X3)
| ( ! [X17] :
( ~ element(X17,X2)
| element(apply(X1,X17),X3) )
& apply(X1,zero(X2)) = zero(X3) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(104,plain,
! [X18,X19,X20] :
( ~ morphism(X18,X19,X20)
| ( ! [X21] :
( ~ element(X21,X19)
| element(apply(X18,X21),X20) )
& apply(X18,zero(X19)) = zero(X20) ) ),
inference(variable_rename,[status(thm)],[103]) ).
fof(105,plain,
! [X18,X19,X20,X21] :
( ( ( ~ element(X21,X19)
| element(apply(X18,X21),X20) )
& apply(X18,zero(X19)) = zero(X20) )
| ~ morphism(X18,X19,X20) ),
inference(shift_quantors,[status(thm)],[104]) ).
fof(106,plain,
! [X18,X19,X20,X21] :
( ( ~ element(X21,X19)
| element(apply(X18,X21),X20)
| ~ morphism(X18,X19,X20) )
& ( apply(X18,zero(X19)) = zero(X20)
| ~ morphism(X18,X19,X20) ) ),
inference(distribute,[status(thm)],[105]) ).
cnf(108,plain,
( element(apply(X1,X4),X3)
| ~ morphism(X1,X2,X3)
| ~ element(X4,X2) ),
inference(split_conjunct,[status(thm)],[106]) ).
fof(111,plain,
! [X19] :
( ~ element(X19,e)
| ? [X20,X21,X22] :
( element(X20,b)
& element(X21,e)
& subtract(e,apply(g,X20),X19) = X21
& element(X22,a)
& apply(gamma,apply(f,X22)) = X21
& apply(g,apply(alpha,X22)) = X21 ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(112,plain,
! [X23] :
( ~ element(X23,e)
| ? [X24,X25,X26] :
( element(X24,b)
& element(X25,e)
& subtract(e,apply(g,X24),X23) = X25
& element(X26,a)
& apply(gamma,apply(f,X26)) = X25
& apply(g,apply(alpha,X26)) = X25 ) ),
inference(variable_rename,[status(thm)],[111]) ).
fof(113,plain,
! [X23] :
( ~ element(X23,e)
| ( element(esk9_1(X23),b)
& element(esk10_1(X23),e)
& subtract(e,apply(g,esk9_1(X23)),X23) = esk10_1(X23)
& element(esk11_1(X23),a)
& apply(gamma,apply(f,esk11_1(X23))) = esk10_1(X23)
& apply(g,apply(alpha,esk11_1(X23))) = esk10_1(X23) ) ),
inference(skolemize,[status(esa)],[112]) ).
fof(114,plain,
! [X23] :
( ( element(esk9_1(X23),b)
| ~ element(X23,e) )
& ( element(esk10_1(X23),e)
| ~ element(X23,e) )
& ( subtract(e,apply(g,esk9_1(X23)),X23) = esk10_1(X23)
| ~ element(X23,e) )
& ( element(esk11_1(X23),a)
| ~ element(X23,e) )
& ( apply(gamma,apply(f,esk11_1(X23))) = esk10_1(X23)
| ~ element(X23,e) )
& ( apply(g,apply(alpha,esk11_1(X23))) = esk10_1(X23)
| ~ element(X23,e) ) ),
inference(distribute,[status(thm)],[113]) ).
cnf(115,plain,
( apply(g,apply(alpha,esk11_1(X1))) = esk10_1(X1)
| ~ element(X1,e) ),
inference(split_conjunct,[status(thm)],[114]) ).
cnf(117,plain,
( element(esk11_1(X1),a)
| ~ element(X1,e) ),
inference(split_conjunct,[status(thm)],[114]) ).
cnf(118,plain,
( subtract(e,apply(g,esk9_1(X1)),X1) = esk10_1(X1)
| ~ element(X1,e) ),
inference(split_conjunct,[status(thm)],[114]) ).
cnf(120,plain,
( element(esk9_1(X1),b)
| ~ element(X1,e) ),
inference(split_conjunct,[status(thm)],[114]) ).
cnf(124,plain,
morphism(g,b,e),
inference(split_conjunct,[status(thm)],[20]) ).
cnf(134,plain,
morphism(alpha,a,b),
inference(split_conjunct,[status(thm)],[22]) ).
fof(136,negated_conjecture,
? [X19] :
( element(X19,e)
& ! [X20,X24] :
( ~ element(X20,b)
| ~ element(X24,b)
| apply(g,subtract(b,X20,X24)) != X19 ) ),
inference(fof_nnf,[status(thm)],[34]) ).
fof(137,negated_conjecture,
? [X25] :
( element(X25,e)
& ! [X26,X27] :
( ~ element(X26,b)
| ~ element(X27,b)
| apply(g,subtract(b,X26,X27)) != X25 ) ),
inference(variable_rename,[status(thm)],[136]) ).
fof(138,negated_conjecture,
( element(esk14_0,e)
& ! [X26,X27] :
( ~ element(X26,b)
| ~ element(X27,b)
| apply(g,subtract(b,X26,X27)) != esk14_0 ) ),
inference(skolemize,[status(esa)],[137]) ).
fof(139,negated_conjecture,
! [X26,X27] :
( ( ~ element(X26,b)
| ~ element(X27,b)
| apply(g,subtract(b,X26,X27)) != esk14_0 )
& element(esk14_0,e) ),
inference(shift_quantors,[status(thm)],[138]) ).
cnf(140,negated_conjecture,
element(esk14_0,e),
inference(split_conjunct,[status(thm)],[139]) ).
cnf(141,negated_conjecture,
( apply(g,subtract(b,X1,X2)) != esk14_0
| ~ element(X2,b)
| ~ element(X1,b) ),
inference(split_conjunct,[status(thm)],[139]) ).
cnf(161,plain,
( element(apply(g,X1),e)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[108,124,theory(equality)]) ).
cnf(166,plain,
( element(apply(alpha,X1),b)
| ~ element(X1,a) ),
inference(spm,[status(thm)],[108,134,theory(equality)]) ).
cnf(172,plain,
( subtract(e,apply(g,esk9_1(X1)),esk10_1(X1)) = X1
| ~ element(X1,e)
| ~ element(apply(g,esk9_1(X1)),e) ),
inference(spm,[status(thm)],[60,118,theory(equality)]) ).
cnf(202,plain,
( subtract(e,apply(g,X1),apply(g,X2)) = apply(g,subtract(b,X1,X2))
| ~ element(X2,b)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[72,124,theory(equality)]) ).
cnf(607,plain,
( subtract(e,apply(g,X1),esk10_1(X2)) = apply(g,subtract(b,X1,apply(alpha,esk11_1(X2))))
| ~ element(apply(alpha,esk11_1(X2)),b)
| ~ element(X1,b)
| ~ element(X2,e) ),
inference(spm,[status(thm)],[202,115,theory(equality)]) ).
cnf(8190,negated_conjecture,
( subtract(e,apply(g,X1),esk10_1(X2)) != esk14_0
| ~ element(apply(alpha,esk11_1(X2)),b)
| ~ element(X1,b)
| ~ element(X2,e) ),
inference(spm,[status(thm)],[141,607,theory(equality)]) ).
cnf(11691,negated_conjecture,
( X1 != esk14_0
| ~ element(apply(alpha,esk11_1(X1)),b)
| ~ element(esk9_1(X1),b)
| ~ element(X1,e)
| ~ element(apply(g,esk9_1(X1)),e) ),
inference(spm,[status(thm)],[8190,172,theory(equality)]) ).
cnf(13573,negated_conjecture,
( X1 != esk14_0
| ~ element(apply(alpha,esk11_1(X1)),b)
| ~ element(esk9_1(X1),b)
| ~ element(X1,e) ),
inference(csr,[status(thm)],[11691,161]) ).
cnf(13574,negated_conjecture,
( X1 != esk14_0
| ~ element(apply(alpha,esk11_1(X1)),b)
| ~ element(X1,e) ),
inference(csr,[status(thm)],[13573,120]) ).
cnf(13575,negated_conjecture,
( X1 != esk14_0
| ~ element(X1,e)
| ~ element(esk11_1(X1),a) ),
inference(spm,[status(thm)],[13574,166,theory(equality)]) ).
cnf(13576,negated_conjecture,
( X1 != esk14_0
| ~ element(X1,e) ),
inference(csr,[status(thm)],[13575,117]) ).
cnf(13577,negated_conjecture,
$false,
inference(spm,[status(thm)],[13576,140,theory(equality)]) ).
cnf(13627,negated_conjecture,
$false,
13577,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/HAL/HAL006+1.p
% --creating new selector for [HAL001+0.ax]
% -running prover on /tmp/tmp5H0de9/sel_HAL006+1.p_1 with time limit 29
% -prover status Theorem
% Problem HAL006+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/HAL/HAL006+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/HAL/HAL006+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
%
%------------------------------------------------------------------------------