TSTP Solution File: COM008+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : COM008+1 : TPTP v5.0.0. Released v3.2.0.
% 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 05:44:45 EST 2010
% Result : Theorem 1.03s
% Output : CNFRefutation 1.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 10
% Syntax : Number of formulae : 83 ( 18 unt; 0 def)
% Number of atoms : 251 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 301 ( 133 ~; 140 |; 21 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 139 ( 0 sgn 66 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( equalish(X1,X2)
=> transitive_reflexive_rewrite(X1,X2) ),
file('/tmp/tmpxc2sWf/sel_COM008+1.p_1',equality_in_transitive_reflexive_rewrite) ).
fof(2,axiom,
! [X1,X2] :
( transitive_reflexive_rewrite(X1,X2)
=> ( equalish(X1,X2)
| ? [X3] :
( rewrite(X1,X3)
& transitive_reflexive_rewrite(X3,X2) ) ) ),
file('/tmp/tmpxc2sWf/sel_COM008+1.p_1',equalish_or_rewrite) ).
fof(3,axiom,
! [X1,X2,X3] :
( ( transitive_reflexive_rewrite(X1,X2)
& transitive_reflexive_rewrite(X2,X3) )
=> transitive_reflexive_rewrite(X1,X3) ),
file('/tmp/tmpxc2sWf/sel_COM008+1.p_1',transitivity_of_transitive_reflexive_rewrite) ).
fof(4,axiom,
! [X1,X2] :
( equalish(X1,X2)
=> equalish(X2,X1) ),
file('/tmp/tmpxc2sWf/sel_COM008+1.p_1',symmetry) ).
fof(5,axiom,
! [X1,X2,X3] :
( ( rewrite(X1,X2)
& rewrite(X1,X3) )
=> ? [X4] :
( transitive_reflexive_rewrite(X2,X4)
& transitive_reflexive_rewrite(X3,X4) ) ),
file('/tmp/tmpxc2sWf/sel_COM008+1.p_1',lo_cfl) ).
fof(6,axiom,
! [X1] : equalish(X1,X1),
file('/tmp/tmpxc2sWf/sel_COM008+1.p_1',reflexivity) ).
fof(7,axiom,
( transitive_reflexive_rewrite(a,b)
& transitive_reflexive_rewrite(a,c) ),
file('/tmp/tmpxc2sWf/sel_COM008+1.p_1',assumption) ).
fof(8,axiom,
! [X1,X2,X3] :
( ( rewrite(a,X1)
& transitive_reflexive_rewrite(X1,X2)
& transitive_reflexive_rewrite(X1,X3) )
=> ? [X4] :
( transitive_reflexive_rewrite(X2,X4)
& transitive_reflexive_rewrite(X3,X4) ) ),
file('/tmp/tmpxc2sWf/sel_COM008+1.p_1',ih_cfl) ).
fof(9,conjecture,
goal,
file('/tmp/tmpxc2sWf/sel_COM008+1.p_1',goal_to_be_proved) ).
fof(10,axiom,
! [X1] :
( ( transitive_reflexive_rewrite(b,X1)
& transitive_reflexive_rewrite(c,X1) )
=> goal ),
file('/tmp/tmpxc2sWf/sel_COM008+1.p_1',found) ).
fof(12,negated_conjecture,
~ goal,
inference(assume_negation,[status(cth)],[9]) ).
fof(13,negated_conjecture,
~ goal,
inference(fof_simplification,[status(thm)],[12,theory(equality)]) ).
fof(14,plain,
! [X1,X2] :
( ~ equalish(X1,X2)
| transitive_reflexive_rewrite(X1,X2) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(15,plain,
! [X3,X4] :
( ~ equalish(X3,X4)
| transitive_reflexive_rewrite(X3,X4) ),
inference(variable_rename,[status(thm)],[14]) ).
cnf(16,plain,
( transitive_reflexive_rewrite(X1,X2)
| ~ equalish(X1,X2) ),
inference(split_conjunct,[status(thm)],[15]) ).
fof(17,plain,
! [X1,X2] :
( ~ transitive_reflexive_rewrite(X1,X2)
| equalish(X1,X2)
| ? [X3] :
( rewrite(X1,X3)
& transitive_reflexive_rewrite(X3,X2) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(18,plain,
! [X4,X5] :
( ~ transitive_reflexive_rewrite(X4,X5)
| equalish(X4,X5)
| ? [X6] :
( rewrite(X4,X6)
& transitive_reflexive_rewrite(X6,X5) ) ),
inference(variable_rename,[status(thm)],[17]) ).
fof(19,plain,
! [X4,X5] :
( ~ transitive_reflexive_rewrite(X4,X5)
| equalish(X4,X5)
| ( rewrite(X4,esk1_2(X4,X5))
& transitive_reflexive_rewrite(esk1_2(X4,X5),X5) ) ),
inference(skolemize,[status(esa)],[18]) ).
fof(20,plain,
! [X4,X5] :
( ( rewrite(X4,esk1_2(X4,X5))
| equalish(X4,X5)
| ~ transitive_reflexive_rewrite(X4,X5) )
& ( transitive_reflexive_rewrite(esk1_2(X4,X5),X5)
| equalish(X4,X5)
| ~ transitive_reflexive_rewrite(X4,X5) ) ),
inference(distribute,[status(thm)],[19]) ).
cnf(21,plain,
( equalish(X1,X2)
| transitive_reflexive_rewrite(esk1_2(X1,X2),X2)
| ~ transitive_reflexive_rewrite(X1,X2) ),
inference(split_conjunct,[status(thm)],[20]) ).
cnf(22,plain,
( equalish(X1,X2)
| rewrite(X1,esk1_2(X1,X2))
| ~ transitive_reflexive_rewrite(X1,X2) ),
inference(split_conjunct,[status(thm)],[20]) ).
fof(23,plain,
! [X1,X2,X3] :
( ~ transitive_reflexive_rewrite(X1,X2)
| ~ transitive_reflexive_rewrite(X2,X3)
| transitive_reflexive_rewrite(X1,X3) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(24,plain,
! [X4,X5,X6] :
( ~ transitive_reflexive_rewrite(X4,X5)
| ~ transitive_reflexive_rewrite(X5,X6)
| transitive_reflexive_rewrite(X4,X6) ),
inference(variable_rename,[status(thm)],[23]) ).
cnf(25,plain,
( transitive_reflexive_rewrite(X1,X2)
| ~ transitive_reflexive_rewrite(X3,X2)
| ~ transitive_reflexive_rewrite(X1,X3) ),
inference(split_conjunct,[status(thm)],[24]) ).
fof(26,plain,
! [X1,X2] :
( ~ equalish(X1,X2)
| equalish(X2,X1) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(27,plain,
! [X3,X4] :
( ~ equalish(X3,X4)
| equalish(X4,X3) ),
inference(variable_rename,[status(thm)],[26]) ).
cnf(28,plain,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
inference(split_conjunct,[status(thm)],[27]) ).
fof(29,plain,
! [X1,X2,X3] :
( ~ rewrite(X1,X2)
| ~ rewrite(X1,X3)
| ? [X4] :
( transitive_reflexive_rewrite(X2,X4)
& transitive_reflexive_rewrite(X3,X4) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(30,plain,
! [X5,X6,X7] :
( ~ rewrite(X5,X6)
| ~ rewrite(X5,X7)
| ? [X8] :
( transitive_reflexive_rewrite(X6,X8)
& transitive_reflexive_rewrite(X7,X8) ) ),
inference(variable_rename,[status(thm)],[29]) ).
fof(31,plain,
! [X5,X6,X7] :
( ~ rewrite(X5,X6)
| ~ rewrite(X5,X7)
| ( transitive_reflexive_rewrite(X6,esk2_3(X5,X6,X7))
& transitive_reflexive_rewrite(X7,esk2_3(X5,X6,X7)) ) ),
inference(skolemize,[status(esa)],[30]) ).
fof(32,plain,
! [X5,X6,X7] :
( ( transitive_reflexive_rewrite(X6,esk2_3(X5,X6,X7))
| ~ rewrite(X5,X6)
| ~ rewrite(X5,X7) )
& ( transitive_reflexive_rewrite(X7,esk2_3(X5,X6,X7))
| ~ rewrite(X5,X6)
| ~ rewrite(X5,X7) ) ),
inference(distribute,[status(thm)],[31]) ).
cnf(33,plain,
( transitive_reflexive_rewrite(X2,esk2_3(X1,X3,X2))
| ~ rewrite(X1,X2)
| ~ rewrite(X1,X3) ),
inference(split_conjunct,[status(thm)],[32]) ).
cnf(34,plain,
( transitive_reflexive_rewrite(X3,esk2_3(X1,X3,X2))
| ~ rewrite(X1,X2)
| ~ rewrite(X1,X3) ),
inference(split_conjunct,[status(thm)],[32]) ).
fof(35,plain,
! [X2] : equalish(X2,X2),
inference(variable_rename,[status(thm)],[6]) ).
cnf(36,plain,
equalish(X1,X1),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(37,plain,
transitive_reflexive_rewrite(a,c),
inference(split_conjunct,[status(thm)],[7]) ).
cnf(38,plain,
transitive_reflexive_rewrite(a,b),
inference(split_conjunct,[status(thm)],[7]) ).
fof(39,plain,
! [X1,X2,X3] :
( ~ rewrite(a,X1)
| ~ transitive_reflexive_rewrite(X1,X2)
| ~ transitive_reflexive_rewrite(X1,X3)
| ? [X4] :
( transitive_reflexive_rewrite(X2,X4)
& transitive_reflexive_rewrite(X3,X4) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(40,plain,
! [X5,X6,X7] :
( ~ rewrite(a,X5)
| ~ transitive_reflexive_rewrite(X5,X6)
| ~ transitive_reflexive_rewrite(X5,X7)
| ? [X8] :
( transitive_reflexive_rewrite(X6,X8)
& transitive_reflexive_rewrite(X7,X8) ) ),
inference(variable_rename,[status(thm)],[39]) ).
fof(41,plain,
! [X5,X6,X7] :
( ~ rewrite(a,X5)
| ~ transitive_reflexive_rewrite(X5,X6)
| ~ transitive_reflexive_rewrite(X5,X7)
| ( transitive_reflexive_rewrite(X6,esk3_3(X5,X6,X7))
& transitive_reflexive_rewrite(X7,esk3_3(X5,X6,X7)) ) ),
inference(skolemize,[status(esa)],[40]) ).
fof(42,plain,
! [X5,X6,X7] :
( ( transitive_reflexive_rewrite(X6,esk3_3(X5,X6,X7))
| ~ rewrite(a,X5)
| ~ transitive_reflexive_rewrite(X5,X6)
| ~ transitive_reflexive_rewrite(X5,X7) )
& ( transitive_reflexive_rewrite(X7,esk3_3(X5,X6,X7))
| ~ rewrite(a,X5)
| ~ transitive_reflexive_rewrite(X5,X6)
| ~ transitive_reflexive_rewrite(X5,X7) ) ),
inference(distribute,[status(thm)],[41]) ).
cnf(43,plain,
( transitive_reflexive_rewrite(X2,esk3_3(X1,X3,X2))
| ~ transitive_reflexive_rewrite(X1,X2)
| ~ transitive_reflexive_rewrite(X1,X3)
| ~ rewrite(a,X1) ),
inference(split_conjunct,[status(thm)],[42]) ).
cnf(44,plain,
( transitive_reflexive_rewrite(X3,esk3_3(X1,X3,X2))
| ~ transitive_reflexive_rewrite(X1,X2)
| ~ transitive_reflexive_rewrite(X1,X3)
| ~ rewrite(a,X1) ),
inference(split_conjunct,[status(thm)],[42]) ).
cnf(45,negated_conjecture,
~ goal,
inference(split_conjunct,[status(thm)],[13]) ).
fof(46,plain,
! [X1] :
( ~ transitive_reflexive_rewrite(b,X1)
| ~ transitive_reflexive_rewrite(c,X1)
| goal ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(47,plain,
! [X2] :
( ~ transitive_reflexive_rewrite(b,X2)
| ~ transitive_reflexive_rewrite(c,X2)
| goal ),
inference(variable_rename,[status(thm)],[46]) ).
cnf(48,plain,
( goal
| ~ transitive_reflexive_rewrite(c,X1)
| ~ transitive_reflexive_rewrite(b,X1) ),
inference(split_conjunct,[status(thm)],[47]) ).
cnf(54,plain,
transitive_reflexive_rewrite(X1,X1),
inference(spm,[status(thm)],[16,36,theory(equality)]) ).
cnf(55,plain,
( ~ transitive_reflexive_rewrite(b,X1)
| ~ transitive_reflexive_rewrite(c,X1) ),
inference(sr,[status(thm)],[48,45,theory(equality)]) ).
cnf(56,plain,
( transitive_reflexive_rewrite(X1,b)
| ~ transitive_reflexive_rewrite(X1,a) ),
inference(spm,[status(thm)],[25,38,theory(equality)]) ).
cnf(57,plain,
( transitive_reflexive_rewrite(X1,c)
| ~ transitive_reflexive_rewrite(X1,a) ),
inference(spm,[status(thm)],[25,37,theory(equality)]) ).
cnf(61,plain,
( transitive_reflexive_rewrite(X1,esk2_3(X2,X3,X4))
| ~ transitive_reflexive_rewrite(X1,X3)
| ~ rewrite(X2,X3)
| ~ rewrite(X2,X4) ),
inference(spm,[status(thm)],[25,34,theory(equality)]) ).
cnf(65,plain,
( transitive_reflexive_rewrite(X1,esk3_3(X2,X3,X4))
| ~ transitive_reflexive_rewrite(X1,X3)
| ~ rewrite(a,X2)
| ~ transitive_reflexive_rewrite(X2,X3)
| ~ transitive_reflexive_rewrite(X2,X4) ),
inference(spm,[status(thm)],[25,44,theory(equality)]) ).
cnf(66,plain,
( ~ transitive_reflexive_rewrite(b,esk3_3(X1,X2,c))
| ~ rewrite(a,X1)
| ~ transitive_reflexive_rewrite(X1,X2)
| ~ transitive_reflexive_rewrite(X1,c) ),
inference(spm,[status(thm)],[55,43,theory(equality)]) ).
cnf(68,plain,
~ transitive_reflexive_rewrite(b,c),
inference(spm,[status(thm)],[55,54,theory(equality)]) ).
cnf(70,plain,
( ~ transitive_reflexive_rewrite(b,b)
| ~ transitive_reflexive_rewrite(c,a) ),
inference(spm,[status(thm)],[55,56,theory(equality)]) ).
cnf(72,plain,
( $false
| ~ transitive_reflexive_rewrite(c,a) ),
inference(rw,[status(thm)],[70,54,theory(equality)]) ).
cnf(73,plain,
~ transitive_reflexive_rewrite(c,a),
inference(cn,[status(thm)],[72,theory(equality)]) ).
cnf(76,plain,
~ transitive_reflexive_rewrite(b,a),
inference(spm,[status(thm)],[68,57,theory(equality)]) ).
cnf(129,plain,
( ~ rewrite(a,X1)
| ~ transitive_reflexive_rewrite(X1,c)
| ~ transitive_reflexive_rewrite(X1,X2)
| ~ transitive_reflexive_rewrite(b,X2) ),
inference(spm,[status(thm)],[66,65,theory(equality)]) ).
cnf(130,plain,
( equalish(a,X1)
| ~ transitive_reflexive_rewrite(esk1_2(a,X1),c)
| ~ transitive_reflexive_rewrite(b,X2)
| ~ transitive_reflexive_rewrite(esk1_2(a,X1),X2)
| ~ transitive_reflexive_rewrite(a,X1) ),
inference(spm,[status(thm)],[129,22,theory(equality)]) ).
cnf(294,plain,
( equalish(a,c)
| ~ transitive_reflexive_rewrite(esk1_2(a,c),X1)
| ~ transitive_reflexive_rewrite(b,X1)
| ~ transitive_reflexive_rewrite(a,c) ),
inference(spm,[status(thm)],[130,21,theory(equality)]) ).
cnf(298,plain,
( equalish(a,c)
| ~ transitive_reflexive_rewrite(esk1_2(a,c),X1)
| ~ transitive_reflexive_rewrite(b,X1)
| $false ),
inference(rw,[status(thm)],[294,37,theory(equality)]) ).
cnf(299,plain,
( equalish(a,c)
| ~ transitive_reflexive_rewrite(esk1_2(a,c),X1)
| ~ transitive_reflexive_rewrite(b,X1) ),
inference(cn,[status(thm)],[298,theory(equality)]) ).
cnf(315,plain,
( equalish(a,c)
| ~ transitive_reflexive_rewrite(b,esk3_3(X1,X2,X3))
| ~ rewrite(a,X1)
| ~ transitive_reflexive_rewrite(esk1_2(a,c),X2)
| ~ transitive_reflexive_rewrite(X1,X2)
| ~ transitive_reflexive_rewrite(X1,X3) ),
inference(spm,[status(thm)],[299,65,theory(equality)]) ).
cnf(2096,plain,
( equalish(a,c)
| ~ rewrite(a,X1)
| ~ transitive_reflexive_rewrite(esk1_2(a,c),X2)
| ~ transitive_reflexive_rewrite(X1,X2)
| ~ transitive_reflexive_rewrite(X1,b) ),
inference(spm,[status(thm)],[315,43,theory(equality)]) ).
cnf(2108,plain,
( equalish(a,c)
| ~ rewrite(a,X1)
| ~ transitive_reflexive_rewrite(X1,b)
| ~ transitive_reflexive_rewrite(X1,esk2_3(X2,X3,X4))
| ~ rewrite(X2,X3)
| ~ rewrite(X2,X4)
| ~ transitive_reflexive_rewrite(esk1_2(a,c),X3) ),
inference(spm,[status(thm)],[2096,61,theory(equality)]) ).
cnf(7694,plain,
( equalish(a,c)
| ~ rewrite(a,X1)
| ~ rewrite(X2,X3)
| ~ rewrite(X2,X1)
| ~ transitive_reflexive_rewrite(esk1_2(a,c),X3)
| ~ transitive_reflexive_rewrite(X1,b) ),
inference(spm,[status(thm)],[2108,33,theory(equality)]) ).
cnf(11725,plain,
( equalish(a,c)
| ~ rewrite(a,X1)
| ~ rewrite(X2,esk1_2(a,c))
| ~ rewrite(X2,X1)
| ~ transitive_reflexive_rewrite(X1,b) ),
inference(spm,[status(thm)],[7694,54,theory(equality)]) ).
cnf(11798,plain,
( equalish(a,c)
| ~ rewrite(a,X1)
| ~ transitive_reflexive_rewrite(X1,b)
| ~ transitive_reflexive_rewrite(a,c) ),
inference(spm,[status(thm)],[11725,22,theory(equality)]) ).
cnf(11799,plain,
( equalish(a,c)
| ~ rewrite(a,X1)
| ~ transitive_reflexive_rewrite(X1,b)
| $false ),
inference(rw,[status(thm)],[11798,37,theory(equality)]) ).
cnf(11800,plain,
( equalish(a,c)
| ~ rewrite(a,X1)
| ~ transitive_reflexive_rewrite(X1,b) ),
inference(cn,[status(thm)],[11799,theory(equality)]) ).
cnf(11801,plain,
( equalish(a,c)
| equalish(a,X1)
| ~ transitive_reflexive_rewrite(esk1_2(a,X1),b)
| ~ transitive_reflexive_rewrite(a,X1) ),
inference(spm,[status(thm)],[11800,22,theory(equality)]) ).
cnf(11802,plain,
( equalish(a,c)
| equalish(a,b)
| ~ transitive_reflexive_rewrite(a,b) ),
inference(spm,[status(thm)],[11801,21,theory(equality)]) ).
cnf(11815,plain,
( equalish(a,c)
| equalish(a,b)
| $false ),
inference(rw,[status(thm)],[11802,38,theory(equality)]) ).
cnf(11816,plain,
( equalish(a,c)
| equalish(a,b) ),
inference(cn,[status(thm)],[11815,theory(equality)]) ).
cnf(11831,plain,
( equalish(c,a)
| equalish(a,b) ),
inference(spm,[status(thm)],[28,11816,theory(equality)]) ).
cnf(11835,plain,
( transitive_reflexive_rewrite(c,a)
| equalish(a,b) ),
inference(spm,[status(thm)],[16,11831,theory(equality)]) ).
cnf(11836,plain,
equalish(a,b),
inference(sr,[status(thm)],[11835,73,theory(equality)]) ).
cnf(11837,plain,
equalish(b,a),
inference(spm,[status(thm)],[28,11836,theory(equality)]) ).
cnf(11954,plain,
transitive_reflexive_rewrite(b,a),
inference(spm,[status(thm)],[16,11837,theory(equality)]) ).
cnf(11958,plain,
$false,
inference(sr,[status(thm)],[11954,76,theory(equality)]) ).
cnf(11959,plain,
$false,
11958,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/COM/COM008+1.p
% --creating new selector for []
% -running prover on /tmp/tmpxc2sWf/sel_COM008+1.p_1 with time limit 29
% -prover status Theorem
% Problem COM008+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/COM/COM008+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/COM/COM008+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
%
%------------------------------------------------------------------------------