TSTP Solution File: HAL003+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : HAL003+3 : TPTP v5.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 11:35:47 EST 2010
% Result : Theorem 0.29s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 9 unt; 0 def)
% Number of atoms : 117 ( 18 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 142 ( 62 ~; 58 |; 18 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 74 ( 0 sgn 38 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(8,axiom,
! [X2,X4,X5] :
( ( element(X4,X2)
& element(X5,X2) )
=> element(subtract(X2,X4,X5),X2) ),
file('/tmp/tmpdgtd62/sel_HAL003+3.p_1',subtract_in_domain) ).
fof(12,axiom,
! [X1,X2,X3] :
( ( morphism(X1,X2,X3)
& ! [X18] :
( element(X18,X3)
=> ? [X12] :
( element(X12,X2)
& apply(X1,X12) = X18 ) ) )
=> surjection(X1) ),
file('/tmp/tmpdgtd62/sel_HAL003+3.p_1',properties_for_surjection) ).
fof(20,axiom,
morphism(g,b,e),
file('/tmp/tmpdgtd62/sel_HAL003+3.p_1',g_morphism) ).
fof(24,axiom,
! [X19] :
( element(X19,e)
=> ? [X20,X24] :
( element(X20,b)
& element(X24,b)
& apply(g,subtract(b,X20,X24)) = X19 ) ),
file('/tmp/tmpdgtd62/sel_HAL003+3.p_1',lemma12) ).
fof(31,conjecture,
surjection(g),
file('/tmp/tmpdgtd62/sel_HAL003+3.p_1',g_surjection) ).
fof(35,negated_conjecture,
~ surjection(g),
inference(assume_negation,[status(cth)],[31]) ).
fof(36,negated_conjecture,
~ surjection(g),
inference(fof_simplification,[status(thm)],[35,theory(equality)]) ).
fof(75,plain,
! [X2,X4,X5] :
( ~ element(X4,X2)
| ~ element(X5,X2)
| element(subtract(X2,X4,X5),X2) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(76,plain,
! [X6,X7,X8] :
( ~ element(X7,X6)
| ~ element(X8,X6)
| element(subtract(X6,X7,X8),X6) ),
inference(variable_rename,[status(thm)],[75]) ).
cnf(77,plain,
( element(subtract(X1,X2,X3),X1)
| ~ element(X3,X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[76]) ).
fof(98,plain,
! [X1,X2,X3] :
( ~ morphism(X1,X2,X3)
| ? [X18] :
( element(X18,X3)
& ! [X12] :
( ~ element(X12,X2)
| apply(X1,X12) != X18 ) )
| surjection(X1) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(99,plain,
! [X19,X20,X21] :
( ~ morphism(X19,X20,X21)
| ? [X22] :
( element(X22,X21)
& ! [X23] :
( ~ element(X23,X20)
| apply(X19,X23) != X22 ) )
| surjection(X19) ),
inference(variable_rename,[status(thm)],[98]) ).
fof(100,plain,
! [X19,X20,X21] :
( ~ morphism(X19,X20,X21)
| ( element(esk8_3(X19,X20,X21),X21)
& ! [X23] :
( ~ element(X23,X20)
| apply(X19,X23) != esk8_3(X19,X20,X21) ) )
| surjection(X19) ),
inference(skolemize,[status(esa)],[99]) ).
fof(101,plain,
! [X19,X20,X21,X23] :
( ( ( ~ element(X23,X20)
| apply(X19,X23) != esk8_3(X19,X20,X21) )
& element(esk8_3(X19,X20,X21),X21) )
| ~ morphism(X19,X20,X21)
| surjection(X19) ),
inference(shift_quantors,[status(thm)],[100]) ).
fof(102,plain,
! [X19,X20,X21,X23] :
( ( ~ element(X23,X20)
| apply(X19,X23) != esk8_3(X19,X20,X21)
| ~ morphism(X19,X20,X21)
| surjection(X19) )
& ( element(esk8_3(X19,X20,X21),X21)
| ~ morphism(X19,X20,X21)
| surjection(X19) ) ),
inference(distribute,[status(thm)],[101]) ).
cnf(103,plain,
( surjection(X1)
| element(esk8_3(X1,X2,X3),X3)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[102]) ).
cnf(104,plain,
( surjection(X1)
| ~ morphism(X1,X2,X3)
| apply(X1,X4) != esk8_3(X1,X2,X3)
| ~ element(X4,X2) ),
inference(split_conjunct,[status(thm)],[102]) ).
cnf(126,plain,
morphism(g,b,e),
inference(split_conjunct,[status(thm)],[20]) ).
fof(138,plain,
! [X19] :
( ~ element(X19,e)
| ? [X20,X24] :
( element(X20,b)
& element(X24,b)
& apply(g,subtract(b,X20,X24)) = X19 ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(139,plain,
! [X25] :
( ~ element(X25,e)
| ? [X26,X27] :
( element(X26,b)
& element(X27,b)
& apply(g,subtract(b,X26,X27)) = X25 ) ),
inference(variable_rename,[status(thm)],[138]) ).
fof(140,plain,
! [X25] :
( ~ element(X25,e)
| ( element(esk14_1(X25),b)
& element(esk15_1(X25),b)
& apply(g,subtract(b,esk14_1(X25),esk15_1(X25))) = X25 ) ),
inference(skolemize,[status(esa)],[139]) ).
fof(141,plain,
! [X25] :
( ( element(esk14_1(X25),b)
| ~ element(X25,e) )
& ( element(esk15_1(X25),b)
| ~ element(X25,e) )
& ( apply(g,subtract(b,esk14_1(X25),esk15_1(X25))) = X25
| ~ element(X25,e) ) ),
inference(distribute,[status(thm)],[140]) ).
cnf(142,plain,
( apply(g,subtract(b,esk14_1(X1),esk15_1(X1))) = X1
| ~ element(X1,e) ),
inference(split_conjunct,[status(thm)],[141]) ).
cnf(143,plain,
( element(esk15_1(X1),b)
| ~ element(X1,e) ),
inference(split_conjunct,[status(thm)],[141]) ).
cnf(144,plain,
( element(esk14_1(X1),b)
| ~ element(X1,e) ),
inference(split_conjunct,[status(thm)],[141]) ).
cnf(151,negated_conjecture,
~ surjection(g),
inference(split_conjunct,[status(thm)],[36]) ).
cnf(183,plain,
( surjection(X1)
| esk8_3(X1,X2,X3) != apply(X1,subtract(X2,X4,X5))
| ~ morphism(X1,X2,X3)
| ~ element(X5,X2)
| ~ element(X4,X2) ),
inference(spm,[status(thm)],[104,77,theory(equality)]) ).
cnf(588,plain,
( surjection(g)
| esk8_3(g,b,X1) != X2
| ~ element(esk15_1(X2),b)
| ~ element(esk14_1(X2),b)
| ~ morphism(g,b,X1)
| ~ element(X2,e) ),
inference(spm,[status(thm)],[183,142,theory(equality)]) ).
cnf(591,plain,
( esk8_3(g,b,X1) != X2
| ~ element(esk15_1(X2),b)
| ~ element(esk14_1(X2),b)
| ~ morphism(g,b,X1)
| ~ element(X2,e) ),
inference(sr,[status(thm)],[588,151,theory(equality)]) ).
cnf(592,plain,
( esk8_3(g,b,X1) != X2
| ~ element(esk15_1(X2),b)
| ~ element(X2,e)
| ~ morphism(g,b,X1) ),
inference(csr,[status(thm)],[591,144]) ).
cnf(593,plain,
( esk8_3(g,b,X1) != X2
| ~ element(X2,e)
| ~ morphism(g,b,X1) ),
inference(csr,[status(thm)],[592,143]) ).
cnf(594,plain,
( ~ element(esk8_3(g,b,X1),e)
| ~ morphism(g,b,X1) ),
inference(er,[status(thm)],[593,theory(equality)]) ).
cnf(595,plain,
( surjection(g)
| ~ morphism(g,b,e) ),
inference(spm,[status(thm)],[594,103,theory(equality)]) ).
cnf(596,plain,
( surjection(g)
| $false ),
inference(rw,[status(thm)],[595,126,theory(equality)]) ).
cnf(597,plain,
surjection(g),
inference(cn,[status(thm)],[596,theory(equality)]) ).
cnf(598,plain,
$false,
inference(sr,[status(thm)],[597,151,theory(equality)]) ).
cnf(599,plain,
$false,
598,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/HAL/HAL003+3.p
% --creating new selector for [HAL001+0.ax]
% -running prover on /tmp/tmpdgtd62/sel_HAL003+3.p_1 with time limit 29
% -prover status Theorem
% Problem HAL003+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/HAL/HAL003+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/HAL/HAL003+3.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
%
%------------------------------------------------------------------------------