%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW284+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n027.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 05:31:02 PM UTC 2026
% Result : Theorem 13.35s 8.96s
% Output : CNFRefutation 13.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 38 ( 22 unt; 0 def)
% Number of atoms : 64 ( 41 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 48 ( 22 ~; 19 |; 2 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 5 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
fof(conj_0,hypothesis,
! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X3) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_coeff__0,axiom,
! [X15,X5] :
( class_Groups_Ozero(X5)
=> hAPP(c_Polynomial_Ocoeff(X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X15) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__0) ).
fof(fact_pe,axiom,
v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pe) ).
fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(fact_poly__eq__iff,axiom,
! [X7,X6,X5] :
( ( class_Int_Oring__char__0(X5)
& class_Rings_Oidom(X5) )
=> ( c_Polynomial_Opoly(X5,X6) = c_Polynomial_Opoly(X5,X7)
<=> X6 = X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__iff) ).
fof(fact_poly__0,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> hAPP(c_Polynomial_Opoly(X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X4) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__0) ).
fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(conj_1,conjecture,
v_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(c_0_11,plain,
! [X3047,X3048] :
( hAPP(X3048,esk1_2(X3047,X3048)) != hAPP(X3047,esk1_2(X3047,X3048))
| X3048 = X3047 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
fof(c_0_12,hypothesis,
! [X6039] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X6039) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(variable_rename,[status(thm)],[conj_0]) ).
fof(c_0_13,plain,
! [X3241,X3242] :
( ~ class_Groups_Ozero(X3242)
| hAPP(c_Polynomial_Ocoeff(X3242,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3242))),X3241) = c_Groups_Ozero__class_Ozero(X3242) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coeff__0])]) ).
cnf(c_0_14,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,hypothesis,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[fact_pe]) ).
cnf(c_0_18,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]) ).
fof(c_0_19,plain,
! [X3054,X3055,X3056] :
( ( c_Polynomial_Opoly(X3056,X3055) != c_Polynomial_Opoly(X3056,X3054)
| X3055 = X3054
| ~ class_Int_Oring__char__0(X3056)
| ~ class_Rings_Oidom(X3056) )
& ( X3055 != X3054
| c_Polynomial_Opoly(X3056,X3055) = c_Polynomial_Opoly(X3056,X3054)
| ~ class_Int_Oring__char__0(X3056)
| ~ class_Rings_Oidom(X3056) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__eq__iff])])]) ).
cnf(c_0_20,hypothesis,
( X1 = c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q)
| hAPP(X1,esk1_2(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),X1)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,v_p),X1) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
fof(c_0_22,plain,
! [X3050,X3051] :
( ~ class_Rings_Ocomm__semiring__0(X3051)
| hAPP(c_Polynomial_Opoly(X3051,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3051))),X3050) = c_Groups_Ozero__class_Ozero(X3051) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__0])]) ).
cnf(c_0_23,plain,
( X2 = X3
| c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(X1,X3)
| ~ class_Int_Oring__char__0(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Int_Oring__char__0]) ).
cnf(c_0_25,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oidom]) ).
cnf(c_0_26,hypothesis,
c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q) = c_Polynomial_Ocoeff(tc_Complex_Ocomplex,v_p),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).
fof(c_0_29,negated_conjecture,
v_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_1])]) ).
cnf(c_0_30,plain,
( X1 = X2
| c_Polynomial_Opoly(tc_Complex_Ocomplex,X1) != c_Polynomial_Opoly(tc_Complex_Ocomplex,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_31,hypothesis,
( X1 = c_Polynomial_Ocoeff(tc_Complex_Ocomplex,v_p)
| hAPP(X1,esk1_2(c_Polynomial_Ocoeff(tc_Complex_Ocomplex,v_p),X1)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_26]),c_0_26]) ).
cnf(c_0_32,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),X1) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_17]),c_0_28])]) ).
cnf(c_0_33,negated_conjecture,
v_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_34,hypothesis,
( v_q = X1
| c_Polynomial_Opoly(tc_Complex_Ocomplex,X1) != c_Polynomial_Ocoeff(tc_Complex_Ocomplex,v_p) ),
inference(spm,[status(thm)],[c_0_30,c_0_26]) ).
cnf(c_0_35,hypothesis,
c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p) = c_Polynomial_Ocoeff(tc_Complex_Ocomplex,v_p),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
v_p != v_q,
inference(rw,[status(thm)],[c_0_33,c_0_17]) ).
cnf(c_0_37,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW284+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n027.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 06:33:21 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 13.35/8.96 % Version : CSE_E---1.7
% 13.35/8.96 % Problem : theBenchmark.p
% 13.35/8.96 % SZS status Theorem for theBenchmark.p
% 13.35/8.96 % SZS output start CNFRefutation
% See solution above
% 13.35/9.01 % Total time : 6.559s
%------------------------------------------------------------------------------