TSTP Solution File: SWW247+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWW247+1 : TPTP v5.2.0. Released v5.2.0.
% 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 : Sun Mar 6 15:20:59 EST 2011
% Result : Theorem 7.06s
% Output : CNFRefutation 7.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 9
% Syntax : Number of formulae : 89 ( 19 unt; 0 def)
% Number of atoms : 189 ( 117 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 189 ( 89 ~; 92 |; 0 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 67 ( 9 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(78,axiom,
( class_Rings_Oidom(t_a)
=> ! [X46] :
( X46 != c_Groups_Ozero__class_Ozero(t_a)
=> hAPP(c_Polynomial_Opoly(t_a,v_cs____),X46) = c_Groups_Ozero__class_Ozero(t_a) ) ),
file('/tmp/tmpIm8rE6/sel_SWW247+1.p_1',fact_C) ).
fof(335,axiom,
! [X24,X2,X3,X4] :
( class_Rings_Ocomm__semiring__0(X4)
=> hAPP(c_Polynomial_Opoly(X4,hAPP(hAPP(c_Polynomial_OpCons(X4),X3),X2)),X24) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X24),hAPP(c_Polynomial_Opoly(X4,X2),X24))) ),
file('/tmp/tmpIm8rE6/sel_SWW247+1.p_1',fact_poly__pCons) ).
fof(603,axiom,
! [X47] :
( class_Rings_Oidom(X47)
=> class_Rings_Ocomm__semiring__1(X47) ),
file('/tmp/tmpIm8rE6/sel_SWW247+1.p_1',clrel_Rings_Oidom__Rings_Ocomm__semiring__1) ).
fof(604,axiom,
! [X47] :
( class_Rings_Oidom(X47)
=> class_Rings_Ocomm__semiring__0(X47) ),
file('/tmp/tmpIm8rE6/sel_SWW247+1.p_1',clrel_Rings_Oidom__Rings_Ocomm__semiring__0) ).
fof(719,conjecture,
hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_x____) = hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_y____),
file('/tmp/tmpIm8rE6/sel_SWW247+1.p_1',conj_0) ).
fof(869,axiom,
! [X3,X4] :
( class_Rings_Ocomm__semiring__1(X4)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ozero__class_Ozero(X4)),X3) = c_Groups_Ozero__class_Ozero(X4) ),
file('/tmp/tmpIm8rE6/sel_SWW247+1.p_1',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(901,axiom,
! [X3,X4] :
( class_Rings_Ocomm__semiring__1(X4)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),c_Groups_Ozero__class_Ozero(X4)) = c_Groups_Ozero__class_Ozero(X4) ),
file('/tmp/tmpIm8rE6/sel_SWW247+1.p_1',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(949,axiom,
! [X3,X4] :
( class_Rings_Ocomm__semiring__1(X4)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X3),c_Groups_Ozero__class_Ozero(X4)) = X3 ),
file('/tmp/tmpIm8rE6/sel_SWW247+1.p_1',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(1174,axiom,
class_Rings_Oidom(t_a),
file('/tmp/tmpIm8rE6/sel_SWW247+1.p_1',tfree_0) ).
fof(1215,negated_conjecture,
hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_x____) != hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_y____),
inference(assume_negation,[status(cth)],[719]) ).
fof(1273,negated_conjecture,
hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_x____) != hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_y____),
inference(fof_simplification,[status(thm)],[1215,theory(equality)]) ).
fof(1559,plain,
( ~ class_Rings_Oidom(t_a)
| ! [X46] :
( X46 = c_Groups_Ozero__class_Ozero(t_a)
| hAPP(c_Polynomial_Opoly(t_a,v_cs____),X46) = c_Groups_Ozero__class_Ozero(t_a) ) ),
inference(fof_nnf,[status(thm)],[78]) ).
fof(1560,plain,
( ~ class_Rings_Oidom(t_a)
| ! [X47] :
( X47 = c_Groups_Ozero__class_Ozero(t_a)
| hAPP(c_Polynomial_Opoly(t_a,v_cs____),X47) = c_Groups_Ozero__class_Ozero(t_a) ) ),
inference(variable_rename,[status(thm)],[1559]) ).
fof(1561,plain,
! [X47] :
( X47 = c_Groups_Ozero__class_Ozero(t_a)
| hAPP(c_Polynomial_Opoly(t_a,v_cs____),X47) = c_Groups_Ozero__class_Ozero(t_a)
| ~ class_Rings_Oidom(t_a) ),
inference(shift_quantors,[status(thm)],[1560]) ).
cnf(1562,plain,
( hAPP(c_Polynomial_Opoly(t_a,v_cs____),X1) = c_Groups_Ozero__class_Ozero(t_a)
| X1 = c_Groups_Ozero__class_Ozero(t_a)
| ~ class_Rings_Oidom(t_a) ),
inference(split_conjunct,[status(thm)],[1561]) ).
fof(2412,plain,
! [X24,X2,X3,X4] :
( ~ class_Rings_Ocomm__semiring__0(X4)
| hAPP(c_Polynomial_Opoly(X4,hAPP(hAPP(c_Polynomial_OpCons(X4),X3),X2)),X24) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X24),hAPP(c_Polynomial_Opoly(X4,X2),X24))) ),
inference(fof_nnf,[status(thm)],[335]) ).
fof(2413,plain,
! [X25,X26,X27,X28] :
( ~ class_Rings_Ocomm__semiring__0(X28)
| hAPP(c_Polynomial_Opoly(X28,hAPP(hAPP(c_Polynomial_OpCons(X28),X27),X26)),X25) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X28),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X28),X25),hAPP(c_Polynomial_Opoly(X28,X26),X25))) ),
inference(variable_rename,[status(thm)],[2412]) ).
cnf(2414,plain,
( hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Polynomial_OpCons(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Polynomial_Opoly(X1,X3),X4)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[2413]) ).
fof(3251,plain,
! [X47] :
( ~ class_Rings_Oidom(X47)
| class_Rings_Ocomm__semiring__1(X47) ),
inference(fof_nnf,[status(thm)],[603]) ).
fof(3252,plain,
! [X48] :
( ~ class_Rings_Oidom(X48)
| class_Rings_Ocomm__semiring__1(X48) ),
inference(variable_rename,[status(thm)],[3251]) ).
cnf(3253,plain,
( class_Rings_Ocomm__semiring__1(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[3252]) ).
fof(3254,plain,
! [X47] :
( ~ class_Rings_Oidom(X47)
| class_Rings_Ocomm__semiring__0(X47) ),
inference(fof_nnf,[status(thm)],[604]) ).
fof(3255,plain,
! [X48] :
( ~ class_Rings_Oidom(X48)
| class_Rings_Ocomm__semiring__0(X48) ),
inference(variable_rename,[status(thm)],[3254]) ).
cnf(3256,plain,
( class_Rings_Ocomm__semiring__0(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[3255]) ).
cnf(3627,negated_conjecture,
hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_x____) != hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_y____),
inference(split_conjunct,[status(thm)],[1273]) ).
fof(4123,plain,
! [X3,X4] :
( ~ class_Rings_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ozero__class_Ozero(X4)),X3) = c_Groups_Ozero__class_Ozero(X4) ),
inference(fof_nnf,[status(thm)],[869]) ).
fof(4124,plain,
! [X5,X6] :
( ~ class_Rings_Ocomm__semiring__1(X6)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Ozero__class_Ozero(X6)),X5) = c_Groups_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[4123]) ).
cnf(4125,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[4124]) ).
fof(4214,plain,
! [X3,X4] :
( ~ class_Rings_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),c_Groups_Ozero__class_Ozero(X4)) = c_Groups_Ozero__class_Ozero(X4) ),
inference(fof_nnf,[status(thm)],[901]) ).
fof(4215,plain,
! [X5,X6] :
( ~ class_Rings_Ocomm__semiring__1(X6)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),c_Groups_Ozero__class_Ozero(X6)) = c_Groups_Ozero__class_Ozero(X6) ),
inference(variable_rename,[status(thm)],[4214]) ).
cnf(4216,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[4215]) ).
fof(4354,plain,
! [X3,X4] :
( ~ class_Rings_Ocomm__semiring__1(X4)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X3),c_Groups_Ozero__class_Ozero(X4)) = X3 ),
inference(fof_nnf,[status(thm)],[949]) ).
fof(4355,plain,
! [X5,X6] :
( ~ class_Rings_Ocomm__semiring__1(X6)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6),X5),c_Groups_Ozero__class_Ozero(X6)) = X5 ),
inference(variable_rename,[status(thm)],[4354]) ).
cnf(4356,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[4355]) ).
cnf(5123,plain,
class_Rings_Oidom(t_a),
inference(split_conjunct,[status(thm)],[1174]) ).
cnf(5278,plain,
class_Rings_Ocomm__semiring__1(t_a),
inference(spm,[status(thm)],[3253,5123,theory(equality)]) ).
cnf(5294,plain,
( c_Groups_Ozero__class_Ozero(t_a) = X1
| hAPP(c_Polynomial_Opoly(t_a,v_cs____),X1) = c_Groups_Ozero__class_Ozero(t_a)
| $false ),
inference(rw,[status(thm)],[1562,5123,theory(equality)]) ).
cnf(5295,plain,
( c_Groups_Ozero__class_Ozero(t_a) = X1
| hAPP(c_Polynomial_Opoly(t_a,v_cs____),X1) = c_Groups_Ozero__class_Ozero(t_a) ),
inference(cn,[status(thm)],[5294,theory(equality)]) ).
cnf(32859,negated_conjecture,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_x____),hAPP(c_Polynomial_Opoly(t_a,v_cs____),v_x____))) != hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_y____)
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(spm,[status(thm)],[3627,2414,theory(equality)]) ).
cnf(86073,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),X1),c_Groups_Ozero__class_Ozero(t_a)) = X1,
inference(spm,[status(thm)],[4356,5278,theory(equality)]) ).
cnf(86076,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),X1),c_Groups_Ozero__class_Ozero(t_a)) = c_Groups_Ozero__class_Ozero(t_a),
inference(spm,[status(thm)],[4216,5278,theory(equality)]) ).
cnf(86077,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Ozero__class_Ozero(t_a)),X1) = c_Groups_Ozero__class_Ozero(t_a),
inference(spm,[status(thm)],[4125,5278,theory(equality)]) ).
cnf(86204,negated_conjecture,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_y____),hAPP(c_Polynomial_Opoly(t_a,v_cs____),v_y____))) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_x____),hAPP(c_Polynomial_Opoly(t_a,v_cs____),v_x____)))
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(spm,[status(thm)],[32859,2414,theory(equality)]) ).
cnf(88128,negated_conjecture,
( c_Groups_Ozero__class_Ozero(t_a) = v_x____
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_x____),c_Groups_Ozero__class_Ozero(t_a))) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_y____),hAPP(c_Polynomial_Opoly(t_a,v_cs____),v_y____)))
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(spm,[status(thm)],[86204,5295,theory(equality)]) ).
cnf(88135,negated_conjecture,
( c_Groups_Ozero__class_Ozero(t_a) = v_x____
| v_c____ != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_y____),hAPP(c_Polynomial_Opoly(t_a,v_cs____),v_y____)))
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[88128,86076,theory(equality)]),86073,theory(equality)]) ).
cnf(88140,negated_conjecture,
( c_Groups_Ozero__class_Ozero(t_a) = v_x____
| c_Groups_Ozero__class_Ozero(t_a) = v_y____
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_y____),c_Groups_Ozero__class_Ozero(t_a))) != v_c____
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(spm,[status(thm)],[88135,5295,theory(equality)]) ).
cnf(88147,negated_conjecture,
( c_Groups_Ozero__class_Ozero(t_a) = v_x____
| c_Groups_Ozero__class_Ozero(t_a) = v_y____
| $false
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[88140,86076,theory(equality)]),86073,theory(equality)]) ).
cnf(88148,negated_conjecture,
( c_Groups_Ozero__class_Ozero(t_a) = v_x____
| c_Groups_Ozero__class_Ozero(t_a) = v_y____
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(cn,[status(thm)],[88147,theory(equality)]) ).
cnf(88154,negated_conjecture,
( c_Groups_Ozero__class_Ozero(t_a) = v_y____
| c_Groups_Ozero__class_Ozero(t_a) = v_x____
| ~ class_Rings_Oidom(t_a) ),
inference(spm,[status(thm)],[88148,3256,theory(equality)]) ).
cnf(88155,negated_conjecture,
( c_Groups_Ozero__class_Ozero(t_a) = v_y____
| c_Groups_Ozero__class_Ozero(t_a) = v_x____
| $false ),
inference(rw,[status(thm)],[88154,5123,theory(equality)]) ).
cnf(88156,negated_conjecture,
( c_Groups_Ozero__class_Ozero(t_a) = v_y____
| c_Groups_Ozero__class_Ozero(t_a) = v_x____ ),
inference(cn,[status(thm)],[88155,theory(equality)]) ).
cnf(88157,negated_conjecture,
( c_Groups_Ozero__class_Ozero(t_a) = v_y____
| v_x____ != v_y____ ),
inference(ef,[status(thm)],[88156,theory(equality)]) ).
cnf(88158,negated_conjecture,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),X1),v_x____) = X1
| c_Groups_Ozero__class_Ozero(t_a) = v_y____ ),
inference(spm,[status(thm)],[86073,88156,theory(equality)]) ).
cnf(88161,negated_conjecture,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_x____),X1) = v_x____
| c_Groups_Ozero__class_Ozero(t_a) = v_y____ ),
inference(spm,[status(thm)],[86077,88156,theory(equality)]) ).
cnf(88238,negated_conjecture,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),X1),v_y____) = X1
| v_x____ != v_y____ ),
inference(spm,[status(thm)],[86073,88157,theory(equality)]) ).
cnf(88241,negated_conjecture,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_y____),X1) = v_y____
| v_x____ != v_y____ ),
inference(spm,[status(thm)],[86077,88157,theory(equality)]) ).
cnf(89026,negated_conjecture,
( c_Groups_Ozero__class_Ozero(t_a) = v_x____
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_y____) != v_c____
| ~ class_Rings_Ocomm__semiring__0(t_a)
| v_x____ != v_y____ ),
inference(spm,[status(thm)],[88135,88241,theory(equality)]) ).
cnf(89364,negated_conjecture,
( c_Groups_Ozero__class_Ozero(t_a) = v_x____
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_y____) != v_c____
| v_x____ != v_y____
| ~ class_Rings_Oidom(t_a) ),
inference(spm,[status(thm)],[89026,3256,theory(equality)]) ).
cnf(89365,negated_conjecture,
( c_Groups_Ozero__class_Ozero(t_a) = v_x____
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_y____) != v_c____
| v_x____ != v_y____
| $false ),
inference(rw,[status(thm)],[89364,5123,theory(equality)]) ).
cnf(89366,negated_conjecture,
( c_Groups_Ozero__class_Ozero(t_a) = v_x____
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_y____) != v_c____
| v_x____ != v_y____ ),
inference(cn,[status(thm)],[89365,theory(equality)]) ).
cnf(89521,negated_conjecture,
( c_Groups_Ozero__class_Ozero(t_a) = v_x____
| v_x____ != v_y____ ),
inference(spm,[status(thm)],[89366,88238,theory(equality)]) ).
cnf(89549,negated_conjecture,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),X1),v_x____) = X1
| v_x____ != v_y____ ),
inference(spm,[status(thm)],[86073,89521,theory(equality)]) ).
cnf(89552,negated_conjecture,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_x____),X1) = v_x____
| v_x____ != v_y____ ),
inference(spm,[status(thm)],[86077,89521,theory(equality)]) ).
cnf(90202,negated_conjecture,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_x____) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_y____),hAPP(c_Polynomial_Opoly(t_a,v_cs____),v_y____)))
| ~ class_Rings_Ocomm__semiring__0(t_a)
| v_x____ != v_y____ ),
inference(spm,[status(thm)],[86204,89552,theory(equality)]) ).
cnf(91231,negated_conjecture,
( c_Groups_Ozero__class_Ozero(t_a) = v_y____
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_x____) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_y____),hAPP(c_Polynomial_Opoly(t_a,v_cs____),v_y____)))
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(spm,[status(thm)],[86204,88161,theory(equality)]) ).
cnf(91318,negated_conjecture,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_y____) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_x____)
| v_x____ != v_y____
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(spm,[status(thm)],[90202,88241,theory(equality)]) ).
cnf(91324,negated_conjecture,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_x____) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_y____)
| v_x____ != v_y____
| ~ class_Rings_Oidom(t_a) ),
inference(spm,[status(thm)],[91318,3256,theory(equality)]) ).
cnf(91325,negated_conjecture,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_x____) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_y____)
| v_x____ != v_y____
| $false ),
inference(rw,[status(thm)],[91324,5123,theory(equality)]) ).
cnf(91326,negated_conjecture,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_x____) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_y____)
| v_x____ != v_y____ ),
inference(cn,[status(thm)],[91325,theory(equality)]) ).
cnf(91327,negated_conjecture,
( v_c____ != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_y____)
| v_x____ != v_y____ ),
inference(spm,[status(thm)],[91326,89549,theory(equality)]) ).
cnf(91328,negated_conjecture,
v_x____ != v_y____,
inference(csr,[status(thm)],[91327,88238]) ).
cnf(91970,negated_conjecture,
( c_Groups_Ozero__class_Ozero(t_a) = v_y____
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_y____),c_Groups_Ozero__class_Ozero(t_a))) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_x____)
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(spm,[status(thm)],[91231,5295,theory(equality)]) ).
cnf(91978,negated_conjecture,
( c_Groups_Ozero__class_Ozero(t_a) = v_y____
| v_c____ != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_x____)
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[91970,86076,theory(equality)]),86073,theory(equality)]) ).
cnf(91983,negated_conjecture,
( c_Groups_Ozero__class_Ozero(t_a) = v_y____
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(csr,[status(thm)],[91978,88158]) ).
cnf(91984,negated_conjecture,
( c_Groups_Ozero__class_Ozero(t_a) = v_y____
| ~ class_Rings_Oidom(t_a) ),
inference(spm,[status(thm)],[91983,3256,theory(equality)]) ).
cnf(91985,negated_conjecture,
( c_Groups_Ozero__class_Ozero(t_a) = v_y____
| $false ),
inference(rw,[status(thm)],[91984,5123,theory(equality)]) ).
cnf(91986,negated_conjecture,
c_Groups_Ozero__class_Ozero(t_a) = v_y____,
inference(cn,[status(thm)],[91985,theory(equality)]) ).
cnf(92063,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_y____),X1) = c_Groups_Ozero__class_Ozero(t_a),
inference(rw,[status(thm)],[86077,91986,theory(equality)]) ).
cnf(92064,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_y____),X1) = v_y____,
inference(rw,[status(thm)],[92063,91986,theory(equality)]) ).
cnf(92068,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),X1),v_y____) = X1,
inference(rw,[status(thm)],[86073,91986,theory(equality)]) ).
cnf(92088,negated_conjecture,
( v_y____ = v_x____
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_y____),hAPP(c_Polynomial_Opoly(t_a,v_cs____),v_y____))) != v_c____
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(rw,[status(thm)],[88135,91986,theory(equality)]) ).
cnf(92089,negated_conjecture,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_y____),hAPP(c_Polynomial_Opoly(t_a,v_cs____),v_y____))) != v_c____
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(sr,[status(thm)],[92088,91328,theory(equality)]) ).
cnf(93368,negated_conjecture,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_y____) != v_c____
| ~ class_Rings_Ocomm__semiring__0(t_a) ),
inference(rw,[status(thm)],[92089,92064,theory(equality)]) ).
cnf(93369,negated_conjecture,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_y____) != v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(spm,[status(thm)],[93368,3256,theory(equality)]) ).
cnf(93370,negated_conjecture,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_y____) != v_c____
| $false ),
inference(rw,[status(thm)],[93369,5123,theory(equality)]) ).
cnf(93371,negated_conjecture,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_y____) != v_c____,
inference(cn,[status(thm)],[93370,theory(equality)]) ).
cnf(93814,negated_conjecture,
$false,
inference(rw,[status(thm)],[93371,92068,theory(equality)]) ).
cnf(93815,negated_conjecture,
$false,
inference(cn,[status(thm)],[93814,theory(equality)]) ).
cnf(93816,negated_conjecture,
$false,
93815,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWW/SWW247+1.p
% --creating new selector for []
% -running prover on /tmp/tmpIm8rE6/sel_SWW247+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWW247+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWW/SWW247+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWW/SWW247+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
%
%------------------------------------------------------------------------------