%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG417-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 06:50:10 AM UTC 2026
% Result : Unsatisfiable 7.53s 6.49s
% Output : CNFRefutation 7.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 13 unt; 0 def)
% Number of atoms : 17 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 2 ( 0 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_pCons__0__0_0,axiom,
! [VAR_0] :
( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(VAR_0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(VAR_0)),VAR_0) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(VAR_0))
| ~ class_HOL_Ozero(VAR_0) ),
file('theBenchmark.p',cls_pCons__0__0_0) ).
cnf(c_754,plain,
( c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),A) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))
| ~ class_HOL_Ozero(A) ),
inference(clausify,[status(thm)],[cls_pCons__0__0_0]) ).
fof(cls_kpn_0,axiom,
v_s____ = c_Polynomial_OpCons(v_k____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),
file('theBenchmark.p',cls_kpn_0) ).
cnf(c_794,plain,
v_s____ = c_Polynomial_OpCons(v_k____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[cls_kpn_0]) ).
fof(cls_CHAINED_0_01,axiom,
v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('theBenchmark.p',cls_CHAINED_0_01) ).
cnf(c_819,plain,
v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(clausify,[status(thm)],[cls_CHAINED_0_01]) ).
cnf(c_820,plain,
c_Polynomial_OpCons(v_k____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(paramod,[status(thm)],[c_794,c_819]) ).
fof(cls_conjecture_0,axiom,
v_k____ = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_821,plain,
v_k____ = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_822,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = v_k____,
inference(copy,[status(thm)],[c_821]) ).
fof(clsarity_Complex__Ocomplex__HOL_Ozero,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).
cnf(c_855,plain,
class_HOL_Ozero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__HOL_Ozero]) ).
cnf(c_1818,plain,
c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(resolve,[status(thm)],[c_855,c_754]) ).
cnf(c_1819,plain,
c_Polynomial_OpCons(v_k____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(paramod,[status(thm)],[c_822,c_1818]) ).
cnf(c_1817,plain,
$false,
inference(resolve,[status(thm)],[c_820,c_1819]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG417-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.43 % Computer : n006.cluster.edu
% 0.17/5.43 % Model : x86_64 x86_64
% 0.17/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.43 % Memory : 8046.5625MB
% 0.17/5.43 % OS : Linux 6.8.0-71-generic
% 0.17/5.43 % CPULimit : 300
% 0.17/5.43 % WCLimit : 300
% 0.17/5.43 % DateTime : Sat Sep 26 21:58:32 UTC 2026
% 0.17/5.44 % CPUTime :
% 0.17/5.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.44 % Process 2209698 was started by sandbox2 on n006,
% 0.17/5.44 % Sat Sep 26 21:58:32 2026
% 0.17/5.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/5.47
% 0.17/5.47 % From the command line: assign(max_seconds, 300).
% 7.53/6.49
% 7.53/6.49 % SZS status Unsatisfiable for theBenchmark
% 7.53/6.49
% 7.53/6.49 % Proof 1 at 0.94 (+ 0.06) seconds.
% 7.53/6.49 % Length of proof is 8.
% 7.53/6.49 % Level of proof is 2.
% 7.53/6.49 % Maximum clause weight is 33.000.
% 7.53/6.49 % Given clauses 255.
% 7.53/6.49
% 7.53/6.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------