%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV682-1 : 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 : n007.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 09:08:56 AM UTC 2026
% Result : Unsatisfiable 56.15s 7.65s
% Output : CNFRefutation 56.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% 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 : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 45 ( 15 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_mult__1__left_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_Omonoid__mult(VAR_0) ),
file('theBenchmark.p',cls_mult__1__left_0) ).
cnf(c_366,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B
| ~ class_OrderedGroup_Omonoid__mult(A) ),
inference(clausify,[status(thm)],[cls_mult__1__left_0]) ).
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_368,plain,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult]) ).
cnf(c_488,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_368,c_366]) ).
fof(cls_ATP__Linkup_OCOMBB__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(hAPP(hAPP(c_COMBB(VAR_0,VAR_1,VAR_2),VAR_3),VAR_4),VAR_5) = hAPP(VAR_3,hAPP(VAR_4,VAR_5)),
file('theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
cnf(c_666,plain,
hAPP(hAPP(hAPP(c_COMBB(A,B,C),D),E),F) = hAPP(D,hAPP(E,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(hAPP(hAPP(c_COMBS(VAR_0,VAR_1,VAR_2),VAR_3),VAR_4),VAR_5) = hAPP(hAPP(VAR_3,VAR_5),hAPP(VAR_4,VAR_5)),
file('theBenchmark.p',cls_ATP__Linkup_OCOMBS__def_0) ).
cnf(c_668,plain,
hAPP(hAPP(hAPP(c_COMBS(A,B,C),D),E),F) = hAPP(hAPP(D,F),hAPP(E,F)),
inference(clausify,[status(thm)],[cls_ATP__Linkup_OCOMBS__def_0]) ).
fof(cls_Suc__n__not__n_0,axiom,
! [VAR_0] : hAPP(c_Suc,VAR_0) != VAR_0,
file('theBenchmark.p',cls_Suc__n__not__n_0) ).
cnf(c_763,plain,
hAPP(c_Suc,A) != A,
inference(clausify,[status(thm)],[cls_Suc__n__not__n_0]) ).
cnf(c_1495,plain,
hAPP(hAPP(hAPP(c_COMBS(A,B,C),D),hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),E) = hAPP(hAPP(D,E),E),
inference(paramod,[status(thm)],[c_488,c_668]) ).
cnf(c_13259,plain,
hAPP(hAPP(hAPP(c_COMBS(A,B,C),hAPP(c_COMBB(D,E,F),V6)),hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),V7) = hAPP(V6,hAPP(V7,V7)),
inference(paramod,[status(thm)],[c_1495,c_666]) ).
cnf(c_13261,plain,
A != hAPP(c_Suc,A),
inference(copy,[status(thm)],[c_763]) ).
cnf(c_13260,plain,
$false,
inference(resolve,[status(thm)],[c_13259,c_13261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV682-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 14:44:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3978770 was started by sandbox on n007,
% 0.10/0.37 % Sat Sep 26 14:44:25 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 56.15/7.65
% 56.15/7.65 % given #500 (I,wt=72): 1307 c_Series_Osuminf(hAPP(hAPP(c_COMBS(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),A)),A),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [factor(554,b,c),rewrite([589(26)])].
% 56.15/7.65
% 56.15/7.65 % given #1000 (F,wt=50): 9441 -hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(v_n,A,tc_nat),B,tc_nat)),tc_nat),c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(v_i,A,tc_nat),B,tc_nat))). [para(929(a,1),9298(a,1,1,1,2)),rewrite([929(16)])].
% 56.15/7.65
% 56.15/7.65 % SZS status Unsatisfiable for theBenchmark
% 56.15/7.65
% 56.15/7.65 % Proof 1 at 6.09 (+ 1.05) seconds.
% 56.15/7.65 % Length of proof is 9.
% 56.15/7.65 % Level of proof is 4.
% 56.15/7.65 % Maximum clause weight is 65.000.
% 56.15/7.65 % Given clauses 1194.
% 56.15/7.65
% 56.15/7.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------