%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW213+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 03:07:27 PM UTC 2026
% Result : Theorem 24.82s 3.66s
% Output : CNFRefutation 14.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 12 unt; 0 def)
% Number of atoms : 49 ( 30 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 41 ( 20 ~; 15 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 56 ( 54 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [V_x,V_h,V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),V_x) = hAPP(c_Polynomial_Opoly(T_a,V_p),c_Groups_Oplus__class_Oplus(T_a,V_h,V_x)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [V_h,V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> c_Polynomial_Odegree(T_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)) = c_Polynomial_Odegree(T_a,V_p) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [V_a,V_p] :
? [B_q] :
( ! [B_x] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,B_q),B_x) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_a,B_x))
& c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,B_q) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,V_p) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1181,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1263,hypothesis,
! [B_q] :
( c_Polynomial_Odegree(tc_Complex_Ocomplex,B_q) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)
=> ( ! [B_x] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,B_q),B_x) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,B_x))
=> v_thesis____ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1264,conjecture,
v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1265,negated_conjecture,
~ v_thesis____,
inference(negated_conjecture,[status(cth)],[f1264]) ).
fof(f1272,plain,
! [V_x,V_h,V_p,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),V_x) = hAPP(c_Polynomial_Opoly(T_a,V_p),c_Groups_Oplus__class_Oplus(T_a,V_h,V_x))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f1273,plain,
! [T_a] :
( ! [V_x,V_h,V_p] : hAPP(c_Polynomial_Opoly(T_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),V_x) = hAPP(c_Polynomial_Opoly(T_a,V_p),c_Groups_Oplus__class_Oplus(T_a,V_h,V_x))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(miniscoping,[status(thm)],[f1272]) ).
fof(f1274,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Opoly(X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,X2)),X3) = hAPP(c_Polynomial_Opoly(X0,X1),c_Groups_Oplus__class_Oplus(X0,X2,X3))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[status(thm)],[f1273]) ).
fof(f1311,plain,
! [V_h,V_p,T_a] :
( c_Polynomial_Odegree(T_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)) = c_Polynomial_Odegree(T_a,V_p)
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f1312,plain,
! [T_a] :
( ! [V_h,V_p] : c_Polynomial_Odegree(T_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)) = c_Polynomial_Odegree(T_a,V_p)
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(miniscoping,[status(thm)],[f1311]) ).
fof(f1313,plain,
! [X0,X1,X2] :
( c_Polynomial_Odegree(X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,X2)) = c_Polynomial_Odegree(X0,X1)
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[status(thm)],[f1312]) ).
fof(f1329,plain,
! [V_a,V_p] :
( ! [B_x] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK1_skl(V_p,V_a)),B_x) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_a,B_x))
& c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,sK1_skl(V_p,V_a)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,V_p) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(B_q,sK1_skl(V_p,V_a))],[f20]) ).
fof(f1331,plain,
! [X0,X1,X2] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK1_skl(X0,X1)),X2) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),
inference(cnf_transformation,[status(thm)],[f1329]) ).
fof(f4681,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f1181]) ).
fof(f4820,plain,
! [B_q] :
( v_thesis____
| ? [B_x] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,B_q),B_x) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,B_x))
| c_Polynomial_Odegree(tc_Complex_Ocomplex,B_q) != c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) ),
inference(pre_NNF_transformation,[status(thm)],[f1263]) ).
fof(f4821,plain,
! [B_q] :
( v_thesis____
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,B_q),sK23_skl(B_q)) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,sK23_skl(B_q)))
| c_Polynomial_Odegree(tc_Complex_Ocomplex,B_q) != c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl]),skolemize(B_x,sK23_skl(B_q))],[f4820]) ).
fof(f4822,plain,
! [X0] :
( v_thesis____
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),sK23_skl(X0)) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,sK23_skl(X0)))
| c_Polynomial_Odegree(tc_Complex_Ocomplex,X0) != c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) ),
inference(cnf_transformation,[status(thm)],[f4821]) ).
fof(f4823,plain,
~ v_thesis____,
inference(cnf_transformation,[status(thm)],[f1265]) ).
fof(f5046,plain,
! [X0] :
( v_thesis____
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),sK23_skl(X0)) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK1_skl(v_p,v_z)),sK23_skl(X0))
| c_Polynomial_Odegree(tc_Complex_Ocomplex,X0) != c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) ),
inference(forward_demodulation,[status(thm)],[f1331,f4822]) ).
fof(f5047,plain,
! [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),sK23_skl(X0)) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK1_skl(v_p,v_z)),sK23_skl(X0))
| c_Polynomial_Odegree(tc_Complex_Ocomplex,X0) != c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) ),
inference(backward_subsumption_resolution,[status(thm)],[f5046,f4823]) ).
fof(f5139,plain,
! [X0,X1] : c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,X0,X1)) = c_Polynomial_Odegree(tc_Complex_Ocomplex,X0),
inference(resolution,[status(thm)],[f4681,f1313]) ).
fof(f5140,plain,
! [X0,X1,X2] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,X0,X1)),X2) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),
inference(resolution,[status(thm)],[f4681,f1274]) ).
fof(f5142,plain,
! [X0,X1,X2] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,X0,X1)),X2) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK1_skl(X0,X1)),X2),
inference(forward_demodulation,[status(thm)],[f1331,f5140]) ).
fof(f11837,plain,
! [X0] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,v_p,X0)),sK23_skl(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,v_p,X0))) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK1_skl(v_p,v_z)),sK23_skl(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,v_p,X0))),
inference(resolution,[status(thm)],[f5139,f5047]) ).
fof(f11849,plain,
! [X0] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK1_skl(v_p,X0)),sK23_skl(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,v_p,X0))) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sK1_skl(v_p,v_z)),sK23_skl(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,v_p,X0))),
inference(forward_demodulation,[status(thm)],[f5142,f11837]) ).
fof(f12322,plain,
$false,
inference(equality_resolution,[status(thm)],[f11849]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW213+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.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 09:41:43 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.46 % Drodi V4.1.1
% 24.82/3.66 % Refutation found
% 24.82/3.66 % SZS status Theorem for theBenchmark: Theorem is valid
% 24.82/3.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 14.44/3.73 % Elapsed time: 3.357614 seconds
% 14.44/3.73 % CPU time: 25.732846 seconds
% 14.44/3.73 % Total memory used: 433.521 MB
% 14.44/3.73 % Net memory used: 420.108 MB
%------------------------------------------------------------------------------