%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV878-1 : 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 : n015.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 09:09:16 AM UTC 2026
% Result : Unsatisfiable 40.88s 10.79s
% Output : CNFRefutation 40.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of formulae : 26 ( 14 unt; 0 def)
% Number of atoms : 43 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 37 ( 20 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-4 aty)
% Number of variables : 51 ( 11 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_sup__ge2_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_lessequals(VAR_1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(VAR_0),VAR_2),VAR_1),VAR_0)
| ~ class_Lattices_Oupper__semilattice(VAR_0) ),
file('theBenchmark.p',cls_sup__ge2_0) ).
cnf(c_4,plain,
( c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),B),A)
| ~ class_Lattices_Oupper__semilattice(A) ),
inference(clausify,[status(thm)],[cls_sup__ge2_0]) ).
fof(clsarity_nat__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
file('theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
cnf(c_24,plain,
class_Lattices_Oupper__semilattice(tc_nat),
inference(clausify,[status(thm)],[clsarity_nat__Lattices_Oupper__semilattice]) ).
cnf(c_175,plain,
c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),A),tc_nat),
inference(resolve,[status(thm)],[c_24,c_4]) ).
fof(clsarity_bool__Finite__Set_Ofinite_Ofinite,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
file('theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
cnf(c_202,plain,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
inference(clausify,[status(thm)],[clsarity_bool__Finite__Set_Ofinite_Ofinite]) ).
fof(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
file('theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
cnf(c_210,plain,
class_Orderings_Olinorder(tc_nat),
inference(clausify,[status(thm)],[clsarity_nat__Orderings_Olinorder]) ).
fof(cls_finite_0,axiom,
! [VAR_0,VAR_1] :
( c_Finite__Set_Ofinite(VAR_1,VAR_0)
| ~ class_Finite__Set_Ofinite_Ofinite(VAR_0) ),
file('theBenchmark.p',cls_finite_0) ).
cnf(c_231,plain,
( c_Finite__Set_Ofinite(B,A)
| ~ class_Finite__Set_Ofinite_Ofinite(A) ),
inference(clausify,[status(thm)],[cls_finite_0]) ).
fof(cls_finite__imageI_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_Finite__Set_Ofinite(VAR_1,VAR_2)
| c_Finite__Set_Ofinite(c_Set_Oimage(VAR_0,VAR_1,VAR_2,VAR_3),VAR_3) ),
file('theBenchmark.p',cls_finite__imageI_0) ).
cnf(c_257,plain,
( ~ c_Finite__Set_Ofinite(B,C)
| c_Finite__Set_Ofinite(c_Set_Oimage(A,B,C,D),D) ),
inference(clausify,[status(thm)],[cls_finite__imageI_0]) ).
fof(cls_rangeI_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : c_in(hAPP(VAR_0,VAR_1),c_Set_Oimage(VAR_0,c_Orderings_Otop__class_Otop(tc_fun(VAR_2,tc_bool)),VAR_2,VAR_3),VAR_3),
file('theBenchmark.p',cls_rangeI_0) ).
cnf(c_403,plain,
c_in(hAPP(A,B),c_Set_Oimage(A,c_Orderings_Otop__class_Otop(tc_fun(C,tc_bool)),C,D),D),
inference(clausify,[status(thm)],[cls_rangeI_0]) ).
fof(cls_Max__ge_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_Finite__Set_Ofinite(VAR_2,VAR_0)
| ~ c_in(VAR_1,VAR_2,VAR_0)
| c_lessequals(VAR_1,hAPP(c_Finite__Set_Olinorder__class_OMax(VAR_0),VAR_2),VAR_0)
| ~ class_Orderings_Olinorder(VAR_0) ),
file('theBenchmark.p',cls_Max__ge_0) ).
cnf(c_487,plain,
( ~ c_Finite__Set_Ofinite(C,A)
| ~ c_in(B,C,A)
| c_lessequals(B,hAPP(c_Finite__Set_Olinorder__class_OMax(A),C),A)
| ~ class_Orderings_Olinorder(A) ),
inference(clausify,[status(thm)],[cls_Max__ge_0]) ).
fof(cls_not__less__eq__eq_1,axiom,
! [VAR_0,VAR_1] :
( ~ c_lessequals(c_Suc(VAR_1),VAR_0,tc_nat)
| ~ c_lessequals(VAR_0,VAR_1,tc_nat) ),
file('theBenchmark.p',cls_not__less__eq__eq_1) ).
cnf(c_531,plain,
( ~ c_lessequals(c_Suc(B),A,tc_nat)
| ~ c_lessequals(A,B,tc_nat) ),
inference(clausify,[status(thm)],[cls_not__less__eq__eq_1]) ).
cnf(c_1135,plain,
c_Finite__Set_Ofinite(A,tc_bool),
inference(resolve,[status(thm)],[c_231,c_202]) ).
cnf(c_3157,plain,
~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),c_Suc(B)),B,tc_nat),
inference(resolve,[status(thm)],[c_531,c_175]) ).
cnf(c_8047,plain,
c_Finite__Set_Ofinite(c_Set_Oimage(A,B,tc_bool,C),C),
inference(resolve,[status(thm)],[c_1135,c_257]) ).
cnf(c_13804,plain,
( ~ c_Finite__Set_Ofinite(B,tc_nat)
| ~ c_in(A,B,tc_nat)
| c_lessequals(A,hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),B),tc_nat) ),
inference(resolve,[status(thm)],[c_487,c_210]) ).
cnf(c_13805,plain,
( ~ c_Finite__Set_Ofinite(c_Set_Oimage(A,c_Orderings_Otop__class_Otop(tc_fun(C,tc_bool)),C,tc_nat),tc_nat)
| c_lessequals(hAPP(A,B),hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),c_Set_Oimage(A,c_Orderings_Otop__class_Otop(tc_fun(C,tc_bool)),C,tc_nat)),tc_nat) ),
inference(resolve,[status(thm)],[c_13804,c_403]) ).
cnf(c_13802,plain,
c_lessequals(hAPP(A,B),hAPP(c_Finite__Set_Olinorder__class_OMax(tc_nat),c_Set_Oimage(A,c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)),tc_bool,tc_nat)),tc_nat),
inference(resolve,[status(thm)],[c_13805,c_8047]) ).
cnf(c_13803,plain,
$false,
inference(resolve,[status(thm)],[c_13802,c_3157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV878-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n015.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
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Sat Sep 26 15:09:35 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.38 % Process 163090 was started by sandbox2 on n015,
% 0.09/5.38 % Sat Sep 26 15:09:35 2026
% 0.09/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/5.41
% 0.13/5.41 % From the command line: assign(max_seconds, 300).
% 40.88/10.79
% 40.88/10.79 % given #500 (I,wt=30): 657 c_HOL_Ominus__class_Ominus(c_Suc(A),B,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(A,B,tc_nat)) | -c_lessequals(B,A,tc_nat) # tptp_name(cls_Suc__diff__le_0) # clausal_fof(1). [assumption].
% 40.88/10.79
% 40.88/10.79 % SZS status Unsatisfiable for theBenchmark
% 40.88/10.79
% 40.88/10.79 % Proof 1 at 4.37 (+ 0.71) seconds.
% 40.88/10.79 % Length of proof is 15.
% 40.88/10.79 % Level of proof is 4.
% 40.88/10.79 % Maximum clause weight is 41.000.
% 40.88/10.79 % Given clauses 789.
% 40.88/10.79
% 40.88/10.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------