%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW182+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:07:23 PM UTC 2026
% Result : Theorem 1.95s 0.80s
% Output : CNFRefutation 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 17 unt; 0 def)
% Number of atoms : 61 ( 28 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 41 ( 19 ~; 16 |; 0 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 60 ( 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [V_h,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> c_Polynomial_Osmult(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f68,axiom,
! [V_a,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f77,axiom,
! [V_h,V_p,V_a,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = 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') ).
fof(f998,axiom,
! [T] :
( class_Rings_Ocomm__semiring__0(T)
=> class_Groups_Ocomm__monoid__add(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1147,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1180,conjecture,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),v_h) = c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1181,negated_conjecture,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),v_h) != c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
inference(negated_conjecture,[status(cth)],[f1180]) ).
fof(f1182,hypothesis,
class_Rings_Ocomm__semiring__0(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1186,plain,
! [V_h,T_a] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f1187,plain,
! [T_a] :
( ! [V_h] : c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(miniscoping,[status(thm)],[f1186]) ).
fof(f1188,plain,
! [X0,X1] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[status(thm)],[f1187]) ).
fof(f1328,plain,
! [V_a,T_a] :
( c_Polynomial_Osmult(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f1329,plain,
! [T_a] :
( ! [V_a] : c_Polynomial_Osmult(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(miniscoping,[status(thm)],[f1328]) ).
fof(f1330,plain,
! [X0,X1] :
( c_Polynomial_Osmult(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[status(thm)],[f1329]) ).
fof(f1414,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f68]) ).
fof(f1415,plain,
! [T_a] :
( ! [V_a] : c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(miniscoping,[status(thm)],[f1414]) ).
fof(f1416,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X0,c_Groups_Ozero__class_Ozero(X0),X1) = X1
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[status(thm)],[f1415]) ).
fof(f1437,plain,
! [V_h,V_p,V_a,T_a] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = 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)))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f77]) ).
fof(f1438,plain,
! [T_a] :
( ! [V_h,V_p,V_a] : c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = 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)))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(miniscoping,[status(thm)],[f1437]) ).
fof(f1439,plain,
! [X0,X1,X2,X3] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,c_Polynomial_OpCons(X0,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X3,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X2,X3)),c_Polynomial_OpCons(X0,X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X2,X3)))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[status(thm)],[f1438]) ).
fof(f4413,plain,
! [T] :
( class_Groups_Ocomm__monoid__add(T)
| ~ class_Rings_Ocomm__semiring__0(T) ),
inference(pre_NNF_transformation,[status(thm)],[f998]) ).
fof(f4414,plain,
! [X0] :
( class_Groups_Ocomm__monoid__add(X0)
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[status(thm)],[f4413]) ).
fof(f4611,plain,
! [T_1] :
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ),
inference(pre_NNF_transformation,[status(thm)],[f1147]) ).
fof(f4612,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[status(thm)],[f4611]) ).
fof(f4673,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),v_h) != c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
inference(cnf_transformation,[status(thm)],[f1181]) ).
fof(f4674,plain,
class_Rings_Ocomm__semiring__0(t_a),
inference(cnf_transformation,[status(thm)],[f1182]) ).
fof(f5119,plain,
! [X0] : c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(resolution,[status(thm)],[f1188,f4674]) ).
fof(f5120,plain,
! [X0,X1,X2] : c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,X1),X2) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,X1,X2)),c_Polynomial_OpCons(t_a,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,X1,X2))),
inference(resolution,[status(thm)],[f1439,f4674]) ).
fof(f5121,plain,
! [X0,X1] : 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_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Polynomial_OpCons(t_a,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),X1))),
inference(paramodulation,[status(thm)],[f5119,f5120]) ).
fof(f5123,plain,
! [X0,X1] : 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_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))),
inference(forward_demodulation,[status(thm)],[f5119,f5121]) ).
fof(f5359,plain,
class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(t_a)),
inference(resolution,[status(thm)],[f4612,f4674]) ).
fof(f5406,plain,
class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(t_a)),
inference(resolution,[status(thm)],[f5359,f4414]) ).
fof(f5422,plain,
! [X0] : c_Polynomial_Osmult(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(resolution,[status(thm)],[f1330,f4674]) ).
fof(f5424,plain,
! [X0,X1] : 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_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))),
inference(backward_demodulation,[status(thm)],[f5422,f5123]) ).
fof(f6148,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),X0) = X0,
inference(resolution,[status(thm)],[f1416,f5406]) ).
fof(f6162,plain,
! [X0,X1] : 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(backward_demodulation,[status(thm)],[f6148,f5424]) ).
fof(f6173,plain,
c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) != c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
inference(backward_demodulation,[status(thm)],[f6162,f4673]) ).
fof(f6175,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f6173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW182+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 09:42:46 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.13/0.46 % Drodi V4.1.1
% 1.95/0.80 % Refutation found
% 1.95/0.80 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.95/0.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.07/0.85 % Elapsed time: 0.479723 seconds
% 2.07/0.85 % CPU time: 2.818257 seconds
% 2.07/0.85 % Total memory used: 240.258 MB
% 2.07/0.85 % Net memory used: 238.576 MB
%------------------------------------------------------------------------------