%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW288+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n022.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 : Tue May 5 05:31:03 PM UTC 2026
% Result : Theorem 11.23s 7.61s
% Output : CNFRefutation 11.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 10 unt; 0 def)
% Number of atoms : 31 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 10 ~; 8 |; 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 : 9 ( 1 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact__096p_A_061_A_091_058poly_Ap_A_I0_058_058_Ha_J_058_093_096,axiom,
( ( class_Int_Oring__char__0(t_a)
& class_Rings_Oidom(t_a) )
=> v_p = 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/sandbox/benchmark/theBenchmark.p',fact__096p_A_061_A_091_058poly_Ap_A_I0_058_058_Ha_J_058_093_096) ).
fof(clrel_Int_Oring__char__0__Groups_Ozero,axiom,
! [X89] :
( class_Int_Oring__char__0(X89)
=> class_Groups_Ozero(X89) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Int_Oring__char__0__Groups_Ozero) ).
fof(fact_degree__pCons__0,axiom,
! [X9,X8] :
( class_Groups_Ozero(X8)
=> c_Polynomial_Odegree(X8,c_Polynomial_OpCons(X8,X9,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__pCons__0) ).
fof(tfree_0,hypothesis,
class_Int_Oring__char__0(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).
fof(tfree_1,hypothesis,
class_Rings_Oidom(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_1) ).
fof(conj_0,conjecture,
c_Polynomial_Odegree(t_a,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(c_0_6,plain,
( ~ class_Int_Oring__char__0(t_a)
| ~ class_Rings_Oidom(t_a)
| v_p = 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))) ),
inference(fof_nnf,[status(thm)],[fact__096p_A_061_A_091_058poly_Ap_A_I0_058_058_Ha_J_058_093_096]) ).
fof(c_0_7,plain,
! [X6126] :
( ~ class_Int_Oring__char__0(X6126)
| class_Groups_Ozero(X6126) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Int_Oring__char__0__Groups_Ozero])]) ).
fof(c_0_8,plain,
! [X3211,X3212] :
( ~ class_Groups_Ozero(X3212)
| c_Polynomial_Odegree(X3212,c_Polynomial_OpCons(X3212,X3211,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3212)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__pCons__0])]) ).
cnf(c_0_9,plain,
( v_p = 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_Int_Oring__char__0(t_a)
| ~ class_Rings_Oidom(t_a) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,hypothesis,
class_Int_Oring__char__0(t_a),
inference(split_conjunct,[status(thm)],[tfree_0]) ).
cnf(c_0_11,hypothesis,
class_Rings_Oidom(t_a),
inference(split_conjunct,[status(thm)],[tfree_1]) ).
fof(c_0_12,negated_conjecture,
c_Polynomial_Odegree(t_a,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(c_0_13,plain,
( class_Groups_Ozero(X1)
| ~ class_Int_Oring__char__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( c_Polynomial_Odegree(X1,c_Polynomial_OpCons(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
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))) = v_p,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_11])]) ).
cnf(c_0_16,negated_conjecture,
c_Polynomial_Odegree(t_a,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,hypothesis,
class_Groups_Ozero(t_a),
inference(spm,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_18,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWW288+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n022.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 06:32:36 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 11.23/7.61 % Version : CSE_E---1.7
% 11.23/7.61 % Problem : theBenchmark.p
% 11.23/7.61 % SZS status Theorem for theBenchmark.p
% 11.23/7.61 % SZS output start CNFRefutation
% See solution above
% 11.23/7.65 % Total time : 5.544s
%------------------------------------------------------------------------------