%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV691-1 : 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 09:08:57 AM UTC 2026
% Result : Unsatisfiable 29.88s 4.83s
% Output : CNFRefutation 29.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 19 unt; 0 def)
% Number of atoms : 27 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 10 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-5 aty)
% Number of variables : 69 ( 24 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
cnf(c_9,plain,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring]) ).
fof(cls_inverse__inverse__eq_0,axiom,
! [VAR_0,VAR_1] :
( hAPP(c_HOL_Oinverse__class_Oinverse(VAR_0),hAPP(c_HOL_Oinverse__class_Oinverse(VAR_0),VAR_1)) = VAR_1
| ~ class_Ring__and__Field_Odivision__by__zero(VAR_0)
| ~ class_Ring__and__Field_Odivision__ring(VAR_0) ),
file('theBenchmark.p',cls_inverse__inverse__eq_0) ).
cnf(c_24,plain,
( hAPP(c_HOL_Oinverse__class_Oinverse(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B)) = B
| ~ class_Ring__and__Field_Odivision__by__zero(A)
| ~ class_Ring__and__Field_Odivision__ring(A) ),
inference(clausify,[status(thm)],[cls_inverse__inverse__eq_0]) ).
cnf(c_685,plain,
( hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)) = A
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ),
inference(resolve,[status(thm)],[c_24,c_9]) ).
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_992,plain,
A != hAPP(c_Suc,A),
inference(clausify,[status(thm)],[cls_n__not__Suc__n_0]) ).
cnf(c_993,plain,
hAPP(c_Suc,A) != A,
inference(copy,[status(thm)],[c_992]) ).
fof(cls_COMBB__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_COMBB__def_0) ).
cnf(c_1039,plain,
hAPP(c_COMBB(A,B,C,D,E),F) = hAPP(A,hAPP(B,F)),
inference(clausify,[status(thm)],[cls_COMBB__def_0]) ).
fof(cls_COMBC__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(hAPP(c_COMBC(VAR_0,VAR_1,VAR_2,VAR_3),VAR_4),VAR_5) = hAPP(hAPP(VAR_0,VAR_5),VAR_4),
file('theBenchmark.p',cls_COMBC__def_0) ).
cnf(c_1040,plain,
hAPP(hAPP(c_COMBC(A,B,C,D),E),F) = hAPP(hAPP(A,F),E),
inference(clausify,[status(thm)],[cls_COMBC__def_0]) ).
fof(cls_COMBS__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_COMBS__def_0) ).
cnf(c_1041,plain,
hAPP(c_COMBS(A,B,C,D,E),F) = hAPP(hAPP(A,F),hAPP(B,F)),
inference(clausify,[status(thm)],[cls_COMBS__def_0]) ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
cnf(c_1069,plain,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero]) ).
cnf(c_1311,plain,
hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)) = A,
inference(resolve,[status(thm)],[c_1069,c_685]) ).
cnf(c_3207,plain,
hAPP(c_COMBB(c_Suc,A,B,C,D),E) != hAPP(A,E),
inference(paramod,[status(thm)],[c_1039,c_993]) ).
cnf(c_5384,plain,
hAPP(hAPP(c_COMBC(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A,B,C),D),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),E)) = hAPP(E,D),
inference(paramod,[status(thm)],[c_1311,c_1040]) ).
cnf(c_5758,plain,
hAPP(c_COMBB(c_Suc,c_COMBS(A,B,C,D,E),F,V6,V7),V8) != hAPP(hAPP(A,V8),hAPP(B,V8)),
inference(paramod,[status(thm)],[c_1041,c_3207]) ).
cnf(c_5760,plain,
hAPP(E,D) = hAPP(hAPP(c_COMBC(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A,B,C),D),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),E)),
inference(copy,[status(thm)],[c_5384]) ).
cnf(c_5759,plain,
$false,
inference(resolve,[status(thm)],[c_5758,c_5760]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV691-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n007.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 14:44:55 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 3979531 was started by sandbox on n007,
% 0.15/0.43 % Sat Sep 26 14:44:55 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.26/0.51
% 0.26/0.51 % From the command line: assign(max_seconds, 300).
% 29.88/4.83
% 29.88/4.83 % given #500 (I,wt=105): 1302 -class_OrderedGroup_Ocomm__monoid__add(t_a) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,t_a),A),c_SetInterval_Oord__class_OatLeastLessThan(B,B,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,t_a),C),c_SetInterval_Oord__class_OatLeastLessThan(B,B,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,t_a),D),c_SetInterval_Oord__class_OatLeastLessThan(B,B,tc_nat))) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2(A,D,B,B))) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2(A,C,B,B))). [factor(967,e,f),unit_del(e,1029)].
% 29.88/4.83
% 29.88/4.83 % SZS status Unsatisfiable for theBenchmark
% 29.88/4.83
% 29.88/4.83 % Proof 1 at 3.93 (+ 0.35) seconds.
% 29.88/4.83 % Length of proof is 14.
% 29.88/4.83 % Level of proof is 4.
% 29.88/4.83 % Maximum clause weight is 46.000.
% 29.88/4.83 % Given clauses 550.
% 29.88/4.83
% 29.88/4.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------