%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV582-1 : 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 : 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 09:08:46 AM UTC 2026
% Result : Unsatisfiable 108.96s 17.01s
% Output : CNFRefutation 108.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 20 unt; 0 def)
% Number of atoms : 24 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 9 ~; 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 : 8 ( 8 usr; 2 con; 0-5 aty)
% Number of variables : 92 ( 36 sgn 21 !; 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_461,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_I5_J_0,axiom,
! [VAR_0,VAR_1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),c_HOL_Ozero__class_Ozero(VAR_0)),VAR_1) = VAR_1
| ~ class_Ring__and__Field_Ocomm__semiring__1(VAR_0) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
cnf(c_470,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B
| ~ class_Ring__and__Field_Ocomm__semiring__1(A) ),
inference(clausify,[status(thm)],[cls_class__semiring_Osemiring__rules_I5_J_0]) ).
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_624,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_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_625,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]) ).
cnf(c_1347,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A,
inference(resolve,[status(thm)],[c_461,c_470]) ).
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_1432,plain,
hAPP(c_Suc,A) != A,
inference(clausify,[status(thm)],[cls_Suc__n__not__n_0]) ).
fof(cls_fcomp__apply_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(c_Fun_Ofcomp(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4),VAR_5) = hAPP(VAR_1,hAPP(VAR_0,VAR_5)),
file('theBenchmark.p',cls_fcomp__apply_0) ).
cnf(c_1435,plain,
hAPP(c_Fun_Ofcomp(A,B,C,D,E),F) = hAPP(B,hAPP(A,F)),
inference(clausify,[status(thm)],[cls_fcomp__apply_0]) ).
cnf(c_31038,plain,
hAPP(c_COMBB(A,c_COMBS(B,C,D,E,F),V6,V7,V8),V9) = hAPP(A,hAPP(hAPP(B,V9),hAPP(C,V9))),
inference(paramod,[status(thm)],[c_625,c_624]) ).
cnf(c_1758,plain,
hAPP(A,hAPP(c_COMBS(B,C,D,E,F),V6)) = hAPP(A,hAPP(hAPP(B,V6),hAPP(C,V6))),
inference(paramod,[status(thm)],[c_624,c_31038]) ).
cnf(c_31039,plain,
hAPP(c_Suc,hAPP(c_COMBS(A,B,C,D,E),F)) != hAPP(hAPP(A,F),hAPP(B,F)),
inference(paramod,[status(thm)],[c_1758,c_1432]) ).
cnf(c_8477,plain,
hAPP(hAPP(A,B),hAPP(C,B)) != hAPP(c_Suc,hAPP(c_COMBS(A,C,D,E,F),B)),
inference(copy,[status(thm)],[c_31039]) ).
cnf(c_31040,plain,
hAPP(A,hAPP(B,A)) != hAPP(c_Suc,hAPP(c_COMBS(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B,C,D,E),A)),
inference(paramod,[status(thm)],[c_1347,c_8477]) ).
cnf(c_16030,plain,
hAPP(c_Suc,hAPP(c_COMBS(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A,B,C,D),E)) != hAPP(E,hAPP(A,E)),
inference(copy,[status(thm)],[c_31040]) ).
cnf(c_31036,plain,
hAPP(c_Suc,hAPP(c_COMBS(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A,B,C),D)) != hAPP(D,D),
inference(paramod,[status(thm)],[c_1347,c_16030]) ).
cnf(c_31041,plain,
hAPP(B,hAPP(A,F)) = hAPP(c_Fun_Ofcomp(A,B,C,D,E),F),
inference(copy,[status(thm)],[c_1435]) ).
cnf(c_31037,plain,
$false,
inference(resolve,[status(thm)],[c_31036,c_31041]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV582-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 14:39:12 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2013352 was started by sandbox2 on n001,
% 0.09/0.36 % Sat Sep 26 14:39:12 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.40
% 0.14/0.40 % From the command line: assign(max_seconds, 300).
% 108.96/17.01
% 108.96/17.01 % given #500 (I,wt=24): 1297 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(B,C),D) != hAPP(hAPP(B,C),E) | -c_RealVector_Ovector__space(B,tc_RealDef_Oreal,A) | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = C | D = E. [copy(1296),flip(d)].
% 108.96/17.01
% 108.96/17.01 % given #1000 (T,wt=8): 7523 class_Finite__Set_Ofinite_Ofinite(tc_fun(tc_fun(tc_bool,tc_bool),A)) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(4763,a,837,c)].
% 108.96/17.01
% 108.96/17.01 % given #1500 (F,wt=18): 16512 -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(v_n,B,tc_nat),tc_nat),tc_nat),c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(v_m,B,tc_nat),tc_nat))). [para(1212(a,1),10773(a,1,2))].
% 108.96/17.01
% 108.96/17.01 % given #2000 (T,wt=10): 13744 class_Finite__Set_Ofinite_Ofinite(tc_fun(tc_bool,tc_Option_Ooption(tc_Option_Ooption(tc_Option_Ooption(tc_fun(tc_Option_Ooption(tc_bool),tc_bool)))))). [resolve(11078,a,1899,b)].
% 108.96/17.01
% 108.96/17.01 % given #2500 (F,wt=16): 26240 -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(v_n,B,tc_nat),tc_nat)),tc_nat),hAPP(c_Suc,v_m))). [para(1212(a,1),26222(a,1,1,1,2))].
% 108.96/17.01
% 108.96/17.01 % given #3000 (T,wt=11): 14644 class_Finite__Set_Ofinite_Ofinite(tc_fun(tc_Option_Ooption(tc_Option_Ooption(tc_Option_Ooption(tc_bool))),tc_fun(tc_Option_Ooption(tc_bool),tc_Option_Ooption(tc_bool)))). [resolve(7574,b,6866,a)].
% 108.96/17.01
% 108.96/17.01 % given #3500 (F,wt=19): 28863 -hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,hAPP(c_Suc,C),tc_nat),tc_nat)),tc_nat),c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat))). [para(1212(a,1),28680(a,1,1,1,2))].
% 108.96/17.01
% 108.96/17.01 % SZS status Unsatisfiable for theBenchmark
% 108.96/17.01
% 108.96/17.01 % Proof 1 at 12.73 (+ 2.94) seconds.
% 108.96/17.01 % Length of proof is 12.
% 108.96/17.01 % Level of proof is 5.
% 108.96/17.01 % Maximum clause weight is 22.000.
% 108.96/17.01 % Given clauses 3822.
% 108.96/17.01
% 108.96/17.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------