%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW287+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 : 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 03:07:34 PM UTC 2026
% Result : Theorem 0.36s 0.62s
% Output : CNFRefutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 15 unt; 0 def)
% Number of atoms : 122 ( 91 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 126 ( 50 ~; 53 |; 13 &)
% ( 2 <=>; 7 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 16 ( 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Nat_OSuc(v_n____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [V_x_3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____))))
=> ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),V_x_3) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),V_x_3) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
( ! [B_x] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
=> ( c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1206,conjecture,
( ! [B_x] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( ( v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1207,negated_conjecture,
~ ( ! [B_x] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( ( v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) ),
inference(negated_conjecture,[status(cth)],[f1206]) ).
fof(f1211,plain,
v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f1212,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f1213,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Nat_OSuc(v_n____),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f1223,plain,
! [V_x_3] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),V_x_3) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),V_x_3) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____)))) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f1224,plain,
( ! [V_x_3] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),V_x_3) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),V_x_3) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____)))) ),
inference(miniscoping,[status(thm)],[f1223]) ).
fof(f1225,plain,
! [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____)))) ),
inference(cnf_transformation,[status(thm)],[f1224]) ).
fof(f1226,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [B_x] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),B_x) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
& hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f1227,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK2_skl) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
& hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK2_skl) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(B_x,sK2_skl)],[f1226]) ).
fof(f1228,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK2_skl) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(cnf_transformation,[status(thm)],[f1227]) ).
fof(f1229,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK2_skl) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(cnf_transformation,[status(thm)],[f1227]) ).
fof(f4801,plain,
( ! [B_x] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_x) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<~> ( ( v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1207]) ).
fof(f4802,plain,
( ( ( ( v_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) )
| ? [B_x] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),B_x) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
& hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )
& ( ( v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ! [B_x] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_x) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
inference(NNF_transformation,[status(thm)],[f4801]) ).
fof(f4803,plain,
( ( ( ( v_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)))) )
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK19_skl) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
& hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK19_skl) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )
& ( ( v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| ! [B_x] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_x) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl]),skolemize(B_x,sK19_skl)],[f4802]) ).
fof(f4804,plain,
! [X0] :
( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(cnf_transformation,[status(thm)],[f4803]) ).
fof(f4806,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK19_skl) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(cnf_transformation,[status(thm)],[f4803]) ).
fof(f4808,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK19_skl) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(cnf_transformation,[status(thm)],[f4803]) ).
fof(f5016,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(backward_subsumption_resolution,[status(thm)],[f4804,f1211]) ).
fof(f5018,plain,
c_Nat_OSuc(v_n____) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(backward_demodulation,[status(thm)],[f1213,f1212]) ).
fof(f5020,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____))))
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK19_skl) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(forward_demodulation,[status(thm)],[f1213,f4806]) ).
fof(f5021,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____))))
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK19_skl) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(forward_demodulation,[status(thm)],[f1213,f4808]) ).
fof(f5030,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| c_Nat_OSuc(v_n____) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK2_skl) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(forward_demodulation,[status(thm)],[f1213,f1228]) ).
fof(f5031,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____))))
| c_Nat_OSuc(v_n____) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK2_skl) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(forward_demodulation,[status(thm)],[f1213,f5030]) ).
fof(f5032,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____))))
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK2_skl) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(forward_subsumption_resolution,[status(thm)],[f5031,f5018]) ).
fof(f5033,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____))))
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(forward_demodulation,[status(thm)],[f1213,f5016]) ).
fof(f5034,plain,
! [X0] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X0) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(forward_subsumption_resolution,[status(thm)],[f5033,f1225]) ).
fof(f5043,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p))))
| c_Nat_OSuc(v_n____) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK2_skl) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(forward_demodulation,[status(thm)],[f1213,f1229]) ).
fof(f5044,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____))))
| c_Nat_OSuc(v_n____) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK2_skl) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(forward_demodulation,[status(thm)],[f1213,f5043]) ).
fof(f5045,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____))))
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK2_skl) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(forward_subsumption_resolution,[status(thm)],[f5044,f5018]) ).
fof(f5046,plain,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK19_skl) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK2_skl) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[f5045,f5021]) ).
fof(f5047,plain,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK19_skl) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK2_skl) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[f5045,f5020]) ).
fof(f5052,plain,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK19_skl) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK2_skl) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[f5046,f5034]) ).
fof(f5061,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK2_skl) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(forward_subsumption_resolution,[status(thm)],[f5052,f5047]) ).
fof(f5062,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK2_skl) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(resolution,[status(thm)],[f5061,f5034]) ).
fof(f5063,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Nat_OSuc(v_n____)))),
inference(backward_subsumption_resolution,[status(thm)],[f5032,f5062]) ).
fof(f5064,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),sK19_skl) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(backward_subsumption_resolution,[status(thm)],[f5021,f5063]) ).
fof(f5065,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK19_skl) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(backward_subsumption_resolution,[status(thm)],[f5020,f5063]) ).
fof(f5066,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),sK19_skl) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(resolution,[status(thm)],[f5064,f5034]) ).
fof(f5067,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(forward_demodulation,[status(thm)],[f5065,f5066]) ).
fof(f5068,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f5067]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW287+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n008.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 09:46:24 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.25/0.60 % Drodi V4.1.1
% 0.36/0.62 % Refutation found
% 0.36/0.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.36/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.39/0.71 % Elapsed time: 0.264315 seconds
% 0.39/0.71 % CPU time: 0.363004 seconds
% 0.39/0.71 % Total memory used: 71.545 MB
% 0.39/0.71 % Net memory used: 71.006 MB
%------------------------------------------------------------------------------