%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG402-1 : 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 : n016.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 17.23s 17.88s
% Output : CNFRefutation 17.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 37 ( 27 unt; 0 def)
% Number of atoms : 47 ( 28 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 13 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 39 ( 4 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
cnf(c_82,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(clausify,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring__1]) ).
fof(cls_class__semiring_Osemiring__rules_I9_J_0,axiom,
! [VAR_0,VAR_1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(VAR_0),VAR_1,VAR_0) = c_HOL_Ozero__class_Ozero(VAR_0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(VAR_0) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
cnf(c_96,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A)
| ~ class_Ring__and__Field_Ocomm__semiring__1(A) ),
inference(clausify,[status(thm)],[cls_class__semiring_Osemiring__rules_I9_J_0]) ).
fof(cls_class__semiring_Osemiring__rules_I11_J_0,axiom,
! [VAR_0,VAR_1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(VAR_0),VAR_1,VAR_0) = VAR_1
| ~ class_Ring__and__Field_Ocomm__semiring__1(VAR_0) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
cnf(c_121,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A) = B
| ~ class_Ring__and__Field_Ocomm__semiring__1(A) ),
inference(clausify,[status(thm)],[cls_class__semiring_Osemiring__rules_I11_J_0]) ).
fof(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
! [VAR_0,VAR_1] :
( c_HOL_Oplus__class_Oplus(VAR_1,c_HOL_Ozero__class_Ozero(VAR_0),VAR_0) = VAR_1
| ~ class_Ring__and__Field_Ocomm__semiring__1(VAR_0) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
cnf(c_135,plain,
( c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A) = B
| ~ class_Ring__and__Field_Ocomm__semiring__1(A) ),
inference(clausify,[status(thm)],[cls_class__semiring_Osemiring__rules_I6_J_0]) ).
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_144,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(cls_zero__neq__one_0,axiom,
! [VAR_0] :
( c_HOL_Ozero__class_Ozero(VAR_0) != c_HOL_Oone__class_Oone(VAR_0)
| ~ class_Ring__and__Field_Ozero__neq__one(VAR_0) ),
file('theBenchmark.p',cls_zero__neq__one_0) ).
cnf(c_249,plain,
( c_HOL_Ozero__class_Ozero(A) != c_HOL_Oone__class_Oone(A)
| ~ class_Ring__and__Field_Ozero__neq__one(A) ),
inference(clausify,[status(thm)],[cls_zero__neq__one_0]) ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
cnf(c_251,plain,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one]) ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
cnf(c_414,plain,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult]) ).
fof(cls_power__one_0,axiom,
! [VAR_0,VAR_1] :
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(VAR_0),VAR_1,VAR_0) = c_HOL_Oone__class_Oone(VAR_0)
| ~ class_OrderedGroup_Omonoid__mult(VAR_0) ),
file('theBenchmark.p',cls_power__one_0) ).
cnf(c_418,plain,
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A) = c_HOL_Oone__class_Oone(A)
| ~ class_OrderedGroup_Omonoid__mult(A) ),
inference(clausify,[status(thm)],[cls_power__one_0]) ).
cnf(c_674,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_251,c_249]) ).
cnf(c_800,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = A,
inference(resolve,[status(thm)],[c_144,c_121]) ).
cnf(c_827,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_144,c_96]) ).
cnf(c_911,plain,
c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A,
inference(resolve,[status(thm)],[c_82,c_135]) ).
fof(cls_conjecture_0,axiom,
! [VAR_0,VAR_1] : c_HOL_Otimes__class_Otimes(VAR_0,c_Power_Opower__class_Opower(VAR_0,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(VAR_1,c_Power_Opower__class_Opower(VAR_1,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_999,plain,
c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_Suc__eq__plus1__left_0,axiom,
! [VAR_0] : c_Suc(VAR_0) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),VAR_0,tc_nat),
file('theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
cnf(c_1241,plain,
c_Suc(A) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat),
inference(clausify,[status(thm)],[cls_Suc__eq__plus1__left_0]) ).
cnf(c_1473,plain,
c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_418,c_414]) ).
cnf(c_6223,plain,
c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_1241,c_999]) ).
cnf(c_6224,plain,
c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_911,c_6223]) ).
cnf(c_6225,plain,
c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_1241,c_6224]) ).
cnf(c_1617,plain,
c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_911,c_6225]) ).
cnf(c_6226,plain,
c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_1617,c_800]) ).
cnf(c_6219,plain,
c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_1473,c_6226]) ).
cnf(c_6227,plain,
c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_1617,c_827]) ).
cnf(c_6228,plain,
c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_6219,c_6227]) ).
cnf(c_6229,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(copy,[status(thm)],[c_6228]) ).
cnf(c_6222,plain,
$false,
inference(resolve,[status(thm)],[c_674,c_6229]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG402-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.13/15.62 % CPULimit : 300
% 0.13/15.62 % WCLimit : 300
% 0.13/15.62 % DateTime : Sat Sep 26 21:57:37 UTC 2026
% 0.13/15.62 % CPUTime :
% 0.13/15.63 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/15.63 % Process 3634402 was started by sandbox2 on n013,
% 0.13/15.63 % Sat Sep 26 21:57:37 2026
% 0.13/15.63 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/15.69
% 0.13/15.69 % From the command line: assign(max_seconds, 300).
% 17.23/17.88
% 17.23/17.88 % given #500 (I,wt=29): 1434 c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_HOL_Oord__class_Oless(B,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),tc_Int_Oint). [resolve(374,a,341,a)].
% 17.23/17.88
% 17.23/17.88 % SZS status Unsatisfiable for theBenchmark
% 17.23/17.88
% 17.23/17.88 % Proof 1 at 2.00 (+ 0.17) seconds.
% 17.23/17.88 % Length of proof is 19.
% 17.23/17.88 % Level of proof is 4.
% 17.23/17.88 % Maximum clause weight is 55.000.
% 17.23/17.88 % Given clauses 617.
% 17.23/17.88
% 17.23/17.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------