TSTP Solution File: SWW186+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWW186+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:38:26 EDT 2023
% Result : Theorem 97.37s 13.84s
% Output : CNFRefutation 97.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 55 ( 16 unt; 0 def)
% Number of atoms : 119 ( 79 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 107 ( 43 ~; 39 |; 9 &)
% ( 3 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 92 ( 6 sgn; 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X3,X5,X4] :
( class_Rings_Ocomm__semiring__0(X4)
=> c_Polynomial_OpCons(X4,X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X4,c_Polynomial_OpCons(X4,X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__single) ).
fof(f4,axiom,
! [X3,X6,X5,X4] :
( class_Rings_Ocomm__semiring__0(X4)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X4,c_Polynomial_OpCons(X4,X5,X6),X3) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),c_Polynomial_Osmult(X4,X3,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X4,X6,X3)),c_Polynomial_OpCons(X4,X5,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X4,X6,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__pCons) ).
fof(f5,axiom,
! [X5,X6,X7,X4] :
( class_Rings_Ocomm__semiring__0(X4)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),c_Polynomial_Osmult(X4,X7,X6),c_Polynomial_OpCons(X4,X5,X6))
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__eq__0__lemma) ).
fof(f12,axiom,
! [X10,X11,X12] :
( class_Groups_Ozero(X12)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X12)) = c_Polynomial_OpCons(X12,X11,X10)
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X12)) = X10
& c_Groups_Ozero__class_Ozero(X12) = X11 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).
fof(f1003,axiom,
! [X86] :
( class_Rings_Ocomm__semiring__0(X86)
=> class_Groups_Ozero(X86) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Ocomm__semiring__0__Groups_Ozero) ).
fof(f1179,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1180,axiom,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(f1181,conjecture,
( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
& v_a = c_Groups_Ozero__class_Ozero(t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
fof(f1182,negated_conjecture,
~ ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
& v_a = c_Groups_Ozero__class_Ozero(t_a) ),
inference(negated_conjecture,[],[f1181]) ).
fof(f1183,axiom,
class_Rings_Ocomm__semiring__0(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).
fof(f1185,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__0(X2)
=> c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0) ),
inference(rectify,[],[f3]) ).
fof(f1186,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)),c_Polynomial_OpCons(X3,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0))) ),
inference(rectify,[],[f4]) ).
fof(f1187,plain,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(X3,X0,X1))
=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1 ) ),
inference(rectify,[],[f5]) ).
fof(f1194,plain,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_OpCons(X2,X1,X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 ) ) ),
inference(rectify,[],[f12]) ).
fof(f2179,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Groups_Ozero(X0) ),
inference(rectify,[],[f1003]) ).
fof(f2365,plain,
! [X0,X1,X2] :
( c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0)
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(ennf_transformation,[],[f1185]) ).
fof(f2366,plain,
! [X0,X1,X2,X3] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)),c_Polynomial_OpCons(X3,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f1186]) ).
fof(f2367,plain,
! [X0,X1,X2,X3] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(X3,X0,X1))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f1187]) ).
fof(f2368,plain,
! [X0,X1,X2,X3] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(X3,X0,X1))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(flattening,[],[f2367]) ).
fof(f2376,plain,
! [X0,X1,X2] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_OpCons(X2,X1,X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 ) )
| ~ class_Groups_Ozero(X2) ),
inference(ennf_transformation,[],[f1194]) ).
fof(f3377,plain,
! [X0] :
( class_Groups_Ozero(X0)
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f2179]) ).
fof(f3441,plain,
( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(ennf_transformation,[],[f1179]) ).
fof(f3442,plain,
( v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| v_a != c_Groups_Ozero__class_Ozero(t_a) ),
inference(ennf_transformation,[],[f1182]) ).
fof(f3447,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_OpCons(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 )
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0) ) )
| ~ class_Groups_Ozero(X2) ),
inference(nnf_transformation,[],[f2376]) ).
fof(f3448,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_OpCons(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 )
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0) ) )
| ~ class_Groups_Ozero(X2) ),
inference(flattening,[],[f3447]) ).
fof(f3753,plain,
! [X2,X0,X1] :
( c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0)
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(cnf_transformation,[],[f2365]) ).
fof(f3754,plain,
! [X2,X3,X0,X1] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)),c_Polynomial_OpCons(X3,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f2366]) ).
fof(f3755,plain,
! [X2,X3,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(X3,X0,X1))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(cnf_transformation,[],[f2368]) ).
fof(f3764,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X1
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0)
| ~ class_Groups_Ozero(X2) ),
inference(cnf_transformation,[],[f3448]) ).
fof(f4969,plain,
! [X0] :
( class_Groups_Ozero(X0)
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f3377]) ).
fof(f5139,plain,
( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(cnf_transformation,[],[f3441]) ).
fof(f5140,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),
inference(cnf_transformation,[],[f1180]) ).
fof(f5141,plain,
( v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| v_a != c_Groups_Ozero__class_Ozero(t_a) ),
inference(cnf_transformation,[],[f3442]) ).
fof(f5142,plain,
class_Rings_Ocomm__semiring__0(t_a),
inference(cnf_transformation,[],[f1183]) ).
cnf(c_51,plain,
( ~ class_Rings_Ocomm__semiring__0(X0)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,c_Polynomial_OpCons(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X2) = c_Polynomial_OpCons(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
inference(cnf_transformation,[],[f3753]) ).
cnf(c_52,plain,
( ~ class_Rings_Ocomm__semiring__0(X0)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X2,X1)),c_Polynomial_OpCons(X0,X3,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X2,X1))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,c_Polynomial_OpCons(X0,X3,X2),X1) ),
inference(cnf_transformation,[],[f3754]) ).
cnf(c_53,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X1,X2),c_Polynomial_OpCons(X0,X3,X2)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 ),
inference(cnf_transformation,[],[f3755]) ).
cnf(c_64,plain,
( c_Polynomial_OpCons(X0,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ozero(X0)
| c_Groups_Ozero__class_Ozero(X0) = X1 ),
inference(cnf_transformation,[],[f3764]) ).
cnf(c_1203,plain,
( ~ class_Rings_Ocomm__semiring__0(X0)
| class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f4969]) ).
cnf(c_1373,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = v_p ),
inference(cnf_transformation,[],[f5139]) ).
cnf(c_1374,plain,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(cnf_transformation,[],[f5140]) ).
cnf(c_1375,negated_conjecture,
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != v_p
| c_Groups_Ozero__class_Ozero(t_a) != v_a ),
inference(cnf_transformation,[],[f5141]) ).
cnf(c_1376,plain,
class_Rings_Ocomm__semiring__0(t_a),
inference(cnf_transformation,[],[f5142]) ).
cnf(c_3306,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),X1) = c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
inference(superposition,[status(thm)],[c_1376,c_51]) ).
cnf(c_3324,plain,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,X1,X0)),c_Polynomial_OpCons(t_a,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,X1,X0))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X2,X1),X0),
inference(superposition,[status(thm)],[c_1376,c_52]) ).
cnf(c_3417,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(superposition,[status(thm)],[c_3324,c_1374]) ).
cnf(c_3817,plain,
( ~ class_Rings_Ocomm__semiring__0(t_a)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(superposition,[status(thm)],[c_1374,c_53]) ).
cnf(c_3821,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(global_subsumption_just,[status(thm)],[c_3817,c_1376,c_3817]) ).
cnf(c_3835,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = v_p,
inference(backward_subsumption_resolution,[status(thm)],[c_1373,c_3821]) ).
cnf(c_3955,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,v_p),X1) = c_Polynomial_OpCons(t_a,X0,v_p),
inference(superposition,[status(thm)],[c_3835,c_3306]) ).
cnf(c_4499,plain,
c_Polynomial_OpCons(t_a,v_a,v_p) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(superposition,[status(thm)],[c_3955,c_3417]) ).
cnf(c_4501,plain,
c_Polynomial_OpCons(t_a,v_a,v_p) = v_p,
inference(light_normalisation,[status(thm)],[c_4499,c_3835]) ).
cnf(c_5068,plain,
class_Groups_Ozero(t_a),
inference(superposition,[status(thm)],[c_1376,c_1203]) ).
cnf(c_80905,plain,
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != v_p
| ~ class_Groups_Ozero(t_a)
| c_Groups_Ozero__class_Ozero(t_a) = v_a ),
inference(superposition,[status(thm)],[c_4501,c_64]) ).
cnf(c_80909,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_80905,c_5068,c_3817,c_1373,c_1375,c_1376]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW186+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.15/0.35 % Computer : n028.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun Aug 27 21:22:09 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.22/0.48 Running first-order theorem proving
% 0.22/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 97.37/13.84 % SZS status Started for theBenchmark.p
% 97.37/13.84 % SZS status Theorem for theBenchmark.p
% 97.37/13.84
% 97.37/13.84 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 97.37/13.84
% 97.37/13.84 ------ iProver source info
% 97.37/13.84
% 97.37/13.84 git: date: 2023-05-31 18:12:56 +0000
% 97.37/13.84 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 97.37/13.84 git: non_committed_changes: false
% 97.37/13.84 git: last_make_outside_of_git: false
% 97.37/13.84
% 97.37/13.84 ------ Parsing...
% 97.37/13.84 ------ Clausification by vclausify_rel & Parsing by iProver...
% 97.37/13.84
% 97.37/13.84 ------ Preprocessing... sf_s rm: 5 0s sf_e sf_s rm: 2 0s sf_e
% 97.37/13.84
% 97.37/13.84 ------ Preprocessing...
% 97.37/13.84
% 97.37/13.84 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 97.37/13.84 ------ Proving...
% 97.37/13.84 ------ Problem Properties
% 97.37/13.84
% 97.37/13.84
% 97.37/13.84 clauses 1104
% 97.37/13.84 conjectures 1
% 97.37/13.84 EPR 163
% 97.37/13.84 Horn 1008
% 97.37/13.84 unary 227
% 97.37/13.84 binary 440
% 97.37/13.84 lits 2653
% 97.37/13.84 lits eq 611
% 97.37/13.84 fd_pure 0
% 97.37/13.84 fd_pseudo 0
% 97.37/13.84 fd_cond 36
% 97.37/13.84 fd_pseudo_cond 97
% 97.37/13.84 AC symbols 0
% 97.37/13.84
% 97.37/13.84 ------ Input Options Time Limit: Unbounded
% 97.37/13.84
% 97.37/13.84
% 97.37/13.84 ------
% 97.37/13.84 Current options:
% 97.37/13.84 ------
% 97.37/13.84
% 97.37/13.84
% 97.37/13.84
% 97.37/13.84
% 97.37/13.84 ------ Proving...
% 97.37/13.84
% 97.37/13.84
% 97.37/13.84 % SZS status Theorem for theBenchmark.p
% 97.37/13.84
% 97.37/13.84 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 97.37/13.84
% 97.37/13.84
%------------------------------------------------------------------------------