%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG398-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 : Sun Sep 27 06:50:08 AM UTC 2026
% Result : Unsatisfiable 91.27s 13.03s
% Output : CNFRefutation 91.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 40 ( 30 unt; 0 def)
% Number of atoms : 56 ( 37 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 37 ( 21 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 39 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
cnf(c_2,plain,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero]) ).
fof(cls_eq__divide__eq_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = c_HOL_Ozero__class_Ozero(VAR_0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(VAR_1,VAR_2,VAR_0),VAR_2,VAR_0) = VAR_1
| ~ class_Ring__and__Field_Odivision__by__zero(VAR_0)
| ~ class_Ring__and__Field_Ofield(VAR_0) ),
file('theBenchmark.p',cls_eq__divide__eq_0) ).
cnf(c_14,plain,
( C = c_HOL_Ozero__class_Ozero(A)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),C,A) = B
| ~ class_Ring__and__Field_Odivision__by__zero(A)
| ~ class_Ring__and__Field_Ofield(A) ),
inference(clausify,[status(thm)],[cls_eq__divide__eq_0]) ).
cnf(c_882,plain,
( B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = A
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
inference(resolve,[status(thm)],[c_14,c_2]) ).
cnf(c_883,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = B
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = A
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
inference(copy,[status(thm)],[c_882]) ).
fof(cls_pc0_0,axiom,
c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('theBenchmark.p',cls_pc0_0) ).
cnf(c_1066,plain,
c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[cls_pc0_0]) ).
fof(cls_pqc0_0,axiom,
c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('theBenchmark.p',cls_pqc0_0) ).
cnf(c_1117,plain,
c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[cls_pqc0_0]) ).
cnf(c_1118,plain,
c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),
inference(copy,[status(thm)],[c_1117]) ).
fof(cls_complex__divide__def_0,axiom,
! [VAR_0,VAR_1] : c_HOL_Oinverse__class_Odivide(VAR_0,VAR_1,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(VAR_0,c_HOL_Oinverse__class_Oinverse(VAR_1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('theBenchmark.p',cls_complex__divide__def_0) ).
cnf(c_1148,plain,
c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(A,c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[cls_complex__divide__def_0]) ).
cnf(c_1149,plain,
c_HOL_Otimes__class_Otimes(A,c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),
inference(copy,[status(thm)],[c_1148]) ).
fof(cls_class__semiring_Omul__c_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_HOL_Otimes__class_Otimes(VAR_1,VAR_2,VAR_0) = c_HOL_Otimes__class_Otimes(VAR_2,VAR_1,VAR_0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(VAR_0) ),
file('theBenchmark.p',cls_class__semiring_Omul__c_0) ).
cnf(c_1188,plain,
( c_HOL_Otimes__class_Otimes(B,C,A) = c_HOL_Otimes__class_Otimes(C,B,A)
| ~ class_Ring__and__Field_Ocomm__semiring__1(A) ),
inference(clausify,[status(thm)],[cls_class__semiring_Omul__c_0]) ).
fof(cls_poly__smult_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_Polynomial_Opoly(c_Polynomial_Osmult(VAR_1,VAR_2,VAR_0),VAR_3,VAR_0) = c_HOL_Otimes__class_Otimes(VAR_1,c_Polynomial_Opoly(VAR_2,VAR_3,VAR_0),VAR_0)
| ~ class_Ring__and__Field_Ocomm__semiring__0(VAR_0) ),
file('theBenchmark.p',cls_poly__smult_0) ).
cnf(c_1189,plain,
( c_Polynomial_Opoly(c_Polynomial_Osmult(B,C,A),D,A) = c_HOL_Otimes__class_Otimes(B,c_Polynomial_Opoly(C,D,A),A)
| ~ class_Ring__and__Field_Ocomm__semiring__0(A) ),
inference(clausify,[status(thm)],[cls_poly__smult_0]) ).
fof(cls_conjecture_0,axiom,
c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1193,plain,
c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_16723,plain,
c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_1118,c_1193]) ).
cnf(c_16724,plain,
c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_1118,c_16723]) ).
cnf(c_1194,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),
inference(copy,[status(thm)],[c_16724]) ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
cnf(c_1206,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1]) ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
cnf(c_1207,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0]) ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
cnf(c_1214,plain,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ofield]) ).
cnf(c_1689,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = B
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = A ),
inference(resolve,[status(thm)],[c_1214,c_883]) ).
cnf(c_2006,plain,
c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(B,A,tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_1206,c_1188]) ).
cnf(c_2023,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = A
| c_HOL_Otimes__class_Otimes(A,c_HOL_Oinverse__class_Odivide(B,A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = B ),
inference(paramod,[status(thm)],[c_2006,c_1689]) ).
cnf(c_2024,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_2006,c_1194]) ).
cnf(c_2029,plain,
c_Polynomial_Opoly(c_Polynomial_Osmult(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(A,c_Polynomial_Opoly(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_1207,c_1189]) ).
cnf(c_16725,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_2029,c_2024]) ).
cnf(c_16726,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_2006,c_16725]) ).
cnf(c_2045,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_1149,c_16726]) ).
cnf(c_16727,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_2023,c_2045]) ).
cnf(c_16728,plain,
c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(copy,[status(thm)],[c_16727]) ).
cnf(c_16722,plain,
$false,
inference(resolve,[status(thm)],[c_1066,c_16728]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG398-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n011.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 21:57:44 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1632303 was started by sandbox on n011,
% 0.09/0.37 % Sat Sep 26 21:57:44 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.41
% 0.15/0.41 % From the command line: assign(max_seconds, 300).
% 91.27/13.03
% 91.27/13.03 % given #500 (I,wt=33): 1264 c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(C,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(A,C,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex). [copy(1263),flip(a)].
% 91.27/13.03
% 91.27/13.03 % given #1000 (T,wt=19): 3288 class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))). [resolve(2136,a,1223,b)].
% 91.27/13.03
% 91.27/13.03 % given #1500 (F,wt=43): 14459 -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(C,A,tc_nat),B,tc_nat),tc_nat). [para(1946(a,1),4846(a,2,1))].
% 91.27/13.03
% 91.27/13.03 % SZS status Unsatisfiable for theBenchmark
% 91.27/13.03
% 91.27/13.03 % Proof 1 at 3.87 (+ 0.62) seconds.
% 91.27/13.03 % Length of proof is 23.
% 91.27/13.03 % Level of proof is 5.
% 91.27/13.03 % Maximum clause weight is 53.000.
% 91.27/13.03 % Given clauses 1615.
% 91.27/13.03
% 91.27/13.03 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------