%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWW288+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 : Fri Sep 25 03:26:55 PM UTC 2026
% Result : Theorem 246.91s 34.93s
% Output : Proof 246.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 16 unt; 0 def)
% Number of atoms : 48 ( 18 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 19 ~; 14 |; 1 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 13 ( 2 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f31,axiom,
! [V_a,T_a] :
( class_Groups_Ozero(T_a)
=> c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_degree__pCons__0) ).
fof(f31_nnf,plain,
! [V_a,T_a] :
( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(T_a) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [T_a,V_a] :
( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(T_a) ),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c44,plain,
( c_Polynomial_Odegree(X1,c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X1) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
fof(f1011,axiom,
! [T] :
( class_Int_Oring__char__0(T)
=> class_Groups_Ozero(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Int_Oring__char__0__Groups_Ozero) ).
fof(f1011_nnf,plain,
! [T] :
( class_Groups_Ozero(T)
| ~ class_Int_Oring__char__0(T) ),
inference(nnf_transformation,[status(thm)],[f1011]) ).
fof(f1011_sk,plain,
! [T] :
( class_Groups_Ozero(T)
| ~ class_Int_Oring__char__0(T) ),
inference(skolemisation,[status(esa)],[f1011_nnf]) ).
cnf(c1477,plain,
( class_Groups_Ozero(X0)
| ~ class_Int_Oring__char__0(X0) ),
inference(cnf_transformation,[status(esa)],[f1011_sk]) ).
fof(f1216,hypothesis,
class_Int_Oring__char__0(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
fof(f1216_nnf,plain,
class_Int_Oring__char__0(t_a),
inference(nnf_transformation,[status(thm)],[f1216]) ).
cnf(c1682,plain,
class_Int_Oring__char__0(t_a),
inference(cnf_transformation,[status(esa)],[f1216_nnf]) ).
cnf(p1178,plain,
class_Groups_Ozero(t_a),
inference(resolution,[status(thm)],[c1477,c1682]) ).
cnf(p1216,plain,
c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(resolution,[status(thm)],[c44,p1178]) ).
fof(f5,axiom,
( ( class_Rings_Oidom(t_a)
& class_Int_Oring__char__0(t_a) )
=> c_Polynomial_Odegree(t_a,v_p) = c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096degree_Ap_A_061_Adegree_A_091_0_h6ffab510b17839ed) ).
fof(f5_nnf,plain,
( c_Polynomial_Odegree(t_a,v_p) = c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
| ~ class_Rings_Oidom(t_a)
| ~ class_Int_Oring__char__0(t_a) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
( c_Polynomial_Odegree(t_a,v_p) = c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
| ~ class_Rings_Oidom(t_a)
| ~ class_Int_Oring__char__0(t_a) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c7,plain,
( c_Polynomial_Odegree(t_a,v_p) = c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
| ~ class_Rings_Oidom(t_a)
| ~ class_Int_Oring__char__0(t_a) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p1137,plain,
( c_Polynomial_Odegree(t_a,v_p) = c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
| ~ class_Rings_Oidom(t_a) ),
inference(resolution,[status(thm)],[c1682,c7]) ).
cnf(p1217,plain,
( c_Polynomial_Odegree(t_a,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Oidom(t_a) ),
inference(demodulation,[status(thm)],[p1216,p1137]) ).
fof(f1217,hypothesis,
class_Rings_Oidom(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_1) ).
fof(f1217_nnf,plain,
class_Rings_Oidom(t_a),
inference(nnf_transformation,[status(thm)],[f1217]) ).
cnf(c1683,plain,
class_Rings_Oidom(t_a),
inference(cnf_transformation,[status(esa)],[f1217_nnf]) ).
cnf(p4129,plain,
c_Polynomial_Odegree(t_a,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(resolution,[status(thm)],[p1217,c1683]) ).
fof(f1215,conjecture,
c_Polynomial_Odegree(t_a,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1215_neg,negated_conjecture,
c_Polynomial_Odegree(t_a,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(negated_conjecture,[status(cth)],[f1215]) ).
fof(f1215_nnf,plain,
c_Polynomial_Odegree(t_a,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(nnf_transformation,[status(thm)],[f1215_neg]) ).
fof(f1215_sk,plain,
c_Polynomial_Odegree(t_a,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(skolemisation,[status(esa)],[f1215_nnf]) ).
cnf(c1681,plain,
c_Polynomial_Odegree(t_a,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[status(esa)],[f1215_sk]) ).
cnf(p4130,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(demodulation,[status(thm)],[p4129,c1681]) ).
cnf(p4131,plain,
$false,
inference(equality_resolution,[status(thm)],[p4130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW288+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 21:58:35 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 246.91/34.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 246.91/34.93 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------