%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG428-1 : 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 : n015.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 06:50:11 AM UTC 2026
% Result : Unsatisfiable 20.23s 3.08s
% Output : CNFRefutation 20.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 9 unt; 0 def)
% Number of atoms : 25 ( 13 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 11 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 9 ( 3 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
~ v_thesis____,
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_761,plain,
~ v_thesis____,
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_CHAINED_0,axiom,
c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_762,plain,
c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
cnf(c_763,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),
inference(copy,[status(thm)],[c_762]) ).
fof(cls_that_0,axiom,
! [VAR_0] :
( v_thesis____
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(VAR_0) ),
file('theBenchmark.p',cls_that_0) ).
cnf(c_781,plain,
( v_thesis____
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Suc(A) ),
inference(clausify,[status(thm)],[cls_that_0]) ).
cnf(c_8606,plain,
( v_thesis____
| c_Suc(A) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) ),
inference(copy,[status(thm)],[c_781]) ).
cnf(c_782,plain,
c_Suc(A) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_761,c_8606]) ).
fof(cls_gr0I_0,axiom,
! [VAR_0] :
( VAR_0 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),VAR_0,tc_nat) ),
file('theBenchmark.p',cls_gr0I_0) ).
cnf(c_841,plain,
( A = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) ),
inference(clausify,[status(thm)],[cls_gr0I_0]) ).
cnf(c_842,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = A
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) ),
inference(copy,[status(thm)],[c_841]) ).
fof(cls_Suc__pred_0,axiom,
! [VAR_0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),VAR_0,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(VAR_0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = VAR_0 ),
file('theBenchmark.p',cls_Suc__pred_0) ).
cnf(c_1091,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(A,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = A ),
inference(clausify,[status(thm)],[cls_Suc__pred_0]) ).
cnf(c_3352,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),tc_nat),
inference(resolve,[status(thm)],[c_842,c_763]) ).
cnf(c_8607,plain,
c_Suc(c_HOL_Ominus__class_Ominus(c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_3352,c_1091]) ).
cnf(c_8605,plain,
$false,
inference(resolve,[status(thm)],[c_782,c_8607]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG428-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n015.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 26 22:03:46 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 839766 was started by sandbox on n015,
% 0.10/0.38 % Sat Sep 26 22:03:46 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).
% 20.23/3.08
% 20.23/3.08 % given #500 (I,wt=24): 1122 c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,C,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). [resolve(14,a,12,a)].
% 20.23/3.08
% 20.23/3.08 % SZS status Unsatisfiable for theBenchmark
% 20.23/3.08
% 20.23/3.08 % Proof 1 at 2.22 (+ 0.24) seconds.
% 20.23/3.08 % Length of proof is 10.
% 20.23/3.08 % Level of proof is 3.
% 20.23/3.08 % Maximum clause weight is 39.000.
% 20.23/3.08 % Given clauses 871.
% 20.23/3.08
% 20.23/3.08 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------