%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV692-1 : 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 : n001.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 09:08:57 AM UTC 2026
% Result : Unsatisfiable 112.76s 15.71s
% Output : CNFRefutation 112.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 60 ( 47 unt; 0 def)
% Number of atoms : 73 ( 54 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 35 ( 22 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-5 aty)
% Number of variables : 105 ( 23 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_of__nat__Suc_0,axiom,
! [VAR_0,VAR_1] :
( c_Nat_Osemiring__1__class_Oof__nat(hAPP(c_Suc,VAR_1),VAR_0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),c_HOL_Oone__class_Oone(VAR_0)),c_Nat_Osemiring__1__class_Oof__nat(VAR_1,VAR_0))
| ~ class_Ring__and__Field_Osemiring__1(VAR_0) ),
file('theBenchmark.p',cls_of__nat__Suc_0) ).
cnf(c_18,plain,
( c_Nat_Osemiring__1__class_Oof__nat(hAPP(c_Suc,B),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A))
| ~ class_Ring__and__Field_Osemiring__1(A) ),
inference(clausify,[status(thm)],[cls_of__nat__Suc_0]) ).
fof(clsarity_nat__Ring__and__Field_Osemiring__1,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
cnf(c_19,plain,
class_Ring__and__Field_Osemiring__1(tc_nat),
inference(clausify,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring__1]) ).
fof(cls_of__nat__0_0,axiom,
! [VAR_0] :
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),VAR_0) = c_HOL_Ozero__class_Ozero(VAR_0)
| ~ class_Ring__and__Field_Osemiring__1(VAR_0) ),
file('theBenchmark.p',cls_of__nat__0_0) ).
cnf(c_21,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Ozero__class_Ozero(A)
| ~ class_Ring__and__Field_Osemiring__1(A) ),
inference(clausify,[status(thm)],[cls_of__nat__0_0]) ).
fof(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
cnf(c_132,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(clausify,[status(thm)],[clsarity_nat__OrderedGroup_Ocomm__monoid__add]) ).
fof(cls_comm__monoid__add_Omult__1__right_0,axiom,
! [VAR_0,VAR_1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),VAR_1),c_HOL_Ozero__class_Ozero(VAR_0)) = VAR_1
| ~ class_OrderedGroup_Ocomm__monoid__add(VAR_0) ),
file('theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
cnf(c_134,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B
| ~ class_OrderedGroup_Ocomm__monoid__add(A) ),
inference(clausify,[status(thm)],[cls_comm__monoid__add_Omult__1__right_0]) ).
fof(cls_comm__monoid__add_Omult__commute_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),VAR_1),VAR_2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),VAR_2),VAR_1)
| ~ class_OrderedGroup_Ocomm__monoid__add(VAR_0) ),
file('theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
cnf(c_139,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B)
| ~ class_OrderedGroup_Ocomm__monoid__add(A) ),
inference(clausify,[status(thm)],[cls_comm__monoid__add_Omult__commute_0]) ).
fof(clsarity_nat__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
cnf(c_387,plain,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
inference(clausify,[status(thm)],[clsarity_nat__OrderedGroup_Ocomm__monoid__mult]) ).
fof(cls_mult__1_0,axiom,
! [VAR_0,VAR_1] :
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(VAR_0),c_HOL_Oone__class_Oone(VAR_0)),VAR_1) = VAR_1
| ~ class_OrderedGroup_Ocomm__monoid__mult(VAR_0) ),
file('theBenchmark.p',cls_mult__1_0) ).
cnf(c_388,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B
| ~ class_OrderedGroup_Ocomm__monoid__mult(A) ),
inference(clausify,[status(thm)],[cls_mult__1_0]) ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
cnf(c_390,plain,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult]) ).
cnf(c_464,plain,
hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A) = A,
inference(resolve,[status(thm)],[c_390,c_388]) ).
cnf(c_466,plain,
hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = A,
inference(resolve,[status(thm)],[c_387,c_388]) ).
cnf(c_566,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A),
inference(resolve,[status(thm)],[c_132,c_139]) ).
cnf(c_572,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A,
inference(resolve,[status(thm)],[c_132,c_134]) ).
fof(cls_ATP__Linkup_OCOMBB__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(c_COMBB(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4),VAR_5) = hAPP(VAR_0,hAPP(VAR_1,VAR_5)),
file('theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
cnf(c_619,plain,
hAPP(c_COMBB(A,B,C,D,E),F) = hAPP(A,hAPP(B,F)),
inference(clausify,[status(thm)],[cls_ATP__Linkup_OCOMBB__def_0]) ).
fof(cls_ATP__Linkup_OCOMBS__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(c_COMBS(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4),VAR_5) = hAPP(hAPP(VAR_0,VAR_5),hAPP(VAR_1,VAR_5)),
file('theBenchmark.p',cls_ATP__Linkup_OCOMBS__def_0) ).
cnf(c_621,plain,
hAPP(c_COMBS(A,B,C,D,E),F) = hAPP(hAPP(A,F),hAPP(B,F)),
inference(clausify,[status(thm)],[cls_ATP__Linkup_OCOMBS__def_0]) ).
fof(cls_mult__eq__1__iff_0,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),VAR_0),VAR_1) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('theBenchmark.p',cls_mult__eq__1__iff_0) ).
cnf(c_821,plain,
( A = hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(clausify,[status(thm)],[cls_mult__eq__1__iff_0]) ).
cnf(c_822,plain,
( hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = A
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(copy,[status(thm)],[c_821]) ).
fof(cls_n__not__Suc__n_0,axiom,
! [VAR_0] : VAR_0 != hAPP(c_Suc,VAR_0),
file('theBenchmark.p',cls_n__not__Suc__n_0) ).
cnf(c_847,plain,
A != hAPP(c_Suc,A),
inference(clausify,[status(thm)],[cls_n__not__Suc__n_0]) ).
cnf(c_848,plain,
hAPP(c_Suc,A) != A,
inference(copy,[status(thm)],[c_847]) ).
fof(cls_add__Suc__shift_0,axiom,
! [VAR_0,VAR_1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,VAR_0)),VAR_1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),VAR_0),hAPP(c_Suc,VAR_1)),
file('theBenchmark.p',cls_add__Suc__shift_0) ).
cnf(c_909,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,A)),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(c_Suc,B)),
inference(clausify,[status(thm)],[cls_add__Suc__shift_0]) ).
fof(cls_add__Suc_0,axiom,
! [VAR_0,VAR_1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,VAR_0)),VAR_1) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),VAR_0),VAR_1)),
file('theBenchmark.p',cls_add__Suc_0) ).
cnf(c_922,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,A)),B) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),
inference(clausify,[status(thm)],[cls_add__Suc_0]) ).
cnf(c_923,plain,
hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,A)),B),
inference(copy,[status(thm)],[c_922]) ).
cnf(c_947,plain,
c_Nat_Osemiring__1__class_Oof__nat(hAPP(c_Suc,A),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),
inference(resolve,[status(thm)],[c_18,c_19]) ).
cnf(c_948,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)) = c_Nat_Osemiring__1__class_Oof__nat(hAPP(c_Suc,A),tc_nat),
inference(copy,[status(thm)],[c_947]) ).
cnf(c_951,plain,
c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(resolve,[status(thm)],[c_21,c_19]) ).
cnf(c_1300,plain,
hAPP(c_COMBB(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B,C,D,E),F) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(B,F)),A),
inference(paramod,[status(thm)],[c_619,c_566]) ).
cnf(c_1354,plain,
hAPP(c_COMBS(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A,B,C,D),E) = hAPP(E,hAPP(A,E)),
inference(paramod,[status(thm)],[c_464,c_621]) ).
cnf(c_1628,plain,
hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat),
inference(resolve,[status(thm)],[c_822,c_466]) ).
cnf(c_1790,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))) = hAPP(c_Suc,A),
inference(paramod,[status(thm)],[c_909,c_572]) ).
cnf(c_1823,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,A)),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),
inference(paramod,[status(thm)],[c_923,c_848]) ).
cnf(c_3414,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,A)),c_HOL_Ozero__class_Ozero(tc_nat)) != A,
inference(paramod,[status(thm)],[c_572,c_1823]) ).
cnf(c_3472,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))) != A,
inference(paramod,[status(thm)],[c_909,c_3414]) ).
cnf(c_3932,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = hAPP(c_Suc,A),
inference(paramod,[status(thm)],[c_1628,c_1790]) ).
cnf(c_7173,plain,
hAPP(c_Suc,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A),
inference(paramod,[status(thm)],[c_3932,c_566]) ).
cnf(c_3940,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = hAPP(c_Suc,A),
inference(copy,[status(thm)],[c_7173]) ).
cnf(c_3972,plain,
hAPP(c_Suc,c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)) = c_Nat_Osemiring__1__class_Oof__nat(hAPP(c_Suc,A),tc_nat),
inference(paramod,[status(thm)],[c_3940,c_948]) ).
cnf(c_7174,plain,
hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Nat_Osemiring__1__class_Oof__nat(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
inference(paramod,[status(thm)],[c_951,c_3972]) ).
cnf(c_4007,plain,
c_Nat_Osemiring__1__class_Oof__nat(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),
inference(copy,[status(thm)],[c_7174]) ).
cnf(c_7175,plain,
c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat) = hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),
inference(paramod,[status(thm)],[c_1628,c_4007]) ).
cnf(c_4180,plain,
hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(copy,[status(thm)],[c_7175]) ).
cnf(c_4239,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat)) != A,
inference(paramod,[status(thm)],[c_4180,c_3472]) ).
cnf(c_5050,plain,
hAPP(c_COMBB(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat)),A,B,C,D),E) != hAPP(A,E),
inference(paramod,[status(thm)],[c_1300,c_4239]) ).
cnf(c_7171,plain,
hAPP(c_COMBS(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A,B,C),D) = hAPP(D,D),
inference(paramod,[status(thm)],[c_464,c_1354]) ).
cnf(c_7176,plain,
hAPP(A,E) != hAPP(c_COMBB(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat)),A,B,C,D),E),
inference(copy,[status(thm)],[c_5050]) ).
cnf(c_7172,plain,
$false,
inference(resolve,[status(thm)],[c_7171,c_7176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV692-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 14:52:43 UTC 2026
% 0.12/0.35 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 2037749 was started by sandbox on n001,
% 0.12/0.36 % Sat Sep 26 14:52:43 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.40
% 0.12/0.40 % From the command line: assign(max_seconds, 300).
% 112.76/15.71
% 112.76/15.71 % given #500 (I,wt=35): 1160 hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [factor(502,c,e),unit_del(b,715),unit_del(c,715)].
% 112.76/15.71
% 112.76/15.71 % given #1000 (W,wt=21): 2575 hBOOL(hAPP(c_COMBB(c_lessequals(A,tc_nat),c_Suc,B,C,D),hAPP(c_Suc,A))). [para(619(a,2),2245(a,1))].
% 112.76/15.71
% 112.76/15.71 % SZS status Unsatisfiable for theBenchmark
% 112.76/15.71
% 112.76/15.71 % Proof 1 at 6.02 (+ 1.14) seconds.
% 112.76/15.71 % Length of proof is 41.
% 112.76/15.71 % Level of proof is 10.
% 112.76/15.71 % Maximum clause weight is 30.000.
% 112.76/15.71 % Given clauses 1266.
% 112.76/15.71
% 112.76/15.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------