%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV573-1 : 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 : n006.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 09:08:45 AM UTC 2026
% Result : Unsatisfiable 17.80s 3.01s
% Output : CNFRefutation 17.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 10 unt; 0 def)
% Number of atoms : 14 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 6 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 7 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_of__real__of__nat__eq_0,axiom,
! [VAR_0,VAR_1] :
( c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(VAR_1,tc_RealDef_Oreal),VAR_0) = c_Nat_Osemiring__1__class_Oof__nat(VAR_1,VAR_0)
| ~ class_RealVector_Oreal__algebra__1(VAR_0) ),
file('theBenchmark.p',cls_of__real__of__nat__eq_0) ).
cnf(c_316,plain,
( c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(B,tc_RealDef_Oreal),A) = c_Nat_Osemiring__1__class_Oof__nat(B,A)
| ~ class_RealVector_Oreal__algebra__1(A) ),
inference(clausify,[status(thm)],[cls_of__real__of__nat__eq_0]) ).
fof(clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).
cnf(c_326,plain,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1]) ).
fof(cls_complex__eq__cancel__iff2_2,axiom,
! [VAR_0] : c_Complex_Ocomplex_OComplex(VAR_0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(VAR_0,tc_Complex_Ocomplex),
file('theBenchmark.p',cls_complex__eq__cancel__iff2_2) ).
cnf(c_1425,plain,
c_Complex_Ocomplex_OComplex(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(A,tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[cls_complex__eq__cancel__iff2_2]) ).
fof(cls_conjecture_0,axiom,
c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) != c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1443,plain,
c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) != c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_1659,plain,
c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) != c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_1425,c_1443]) ).
cnf(c_1444,plain,
c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) != c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex),
inference(copy,[status(thm)],[c_1659]) ).
cnf(c_1657,plain,
c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(A,tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_326,c_316]) ).
cnf(c_1658,plain,
$false,
inference(resolve,[status(thm)],[c_1657,c_1444]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV573-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 14:31:26 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 1465550 was started by sandbox on n006,
% 0.10/0.38 % Sat Sep 26 14:31:26 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.42
% 0.10/0.42 % From the command line: assign(max_seconds, 300).
% 17.80/3.01
% 17.80/3.01 % SZS status Unsatisfiable for theBenchmark
% 17.80/3.01
% 17.80/3.01 % Proof 1 at 2.49 (+ 0.02) seconds.
% 17.80/3.01 % Length of proof is 7.
% 17.80/3.01 % Level of proof is 2.
% 17.80/3.01 % Maximum clause weight is 24.000.
% 17.80/3.01 % Given clauses 0.
% 17.80/3.01
% 17.80/3.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------