%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV876-1 : 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 : n008.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 236.39s 31.60s
% Output : CNFRefutation 236.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 36 ( 20 unt; 0 def)
% Number of atoms : 61 ( 3 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 54 ( 29 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-4 aty)
% Number of variables : 69 ( 12 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
file('theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
cnf(c_1,plain,
class_Orderings_Olinorder(tc_nat),
inference(clausify,[status(thm)],[clsarity_nat__Orderings_Olinorder]) ).
fof(cls_Max__ge_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_Finite__Set_Ofinite(VAR_2,VAR_0)
| ~ hBOOL(c_in(VAR_1,VAR_2,VAR_0))
| hBOOL(hAPP(c_lessequals(VAR_1,VAR_0),c_Finite__Set_Olinorder__class_OMax(VAR_2,VAR_0)))
| ~ class_Orderings_Olinorder(VAR_0) ),
file('theBenchmark.p',cls_Max__ge_0) ).
cnf(c_5,plain,
( ~ c_Finite__Set_Ofinite(C,A)
| ~ hBOOL(c_in(B,C,A))
| hBOOL(hAPP(c_lessequals(B,A),c_Finite__Set_Olinorder__class_OMax(C,A)))
| ~ class_Orderings_Olinorder(A) ),
inference(clausify,[status(thm)],[cls_Max__ge_0]) ).
fof(cls_linorder__not__le_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(VAR_2,VAR_0),VAR_1))
| ~ hBOOL(hAPP(c_lessequals(VAR_1,VAR_0),VAR_2))
| ~ class_Orderings_Olinorder(VAR_0) ),
file('theBenchmark.p',cls_linorder__not__le_1) ).
cnf(c_24,plain,
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B))
| ~ hBOOL(hAPP(c_lessequals(B,A),C))
| ~ class_Orderings_Olinorder(A) ),
inference(clausify,[status(thm)],[cls_linorder__not__le_1]) ).
fof(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
cnf(c_132,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
inference(clausify,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le]) ).
fof(cls_add__less__cancel__right_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(VAR_1,VAR_0),VAR_3))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),VAR_1),VAR_2),VAR_0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),VAR_3),VAR_2)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(VAR_0) ),
file('theBenchmark.p',cls_add__less__cancel__right_1) ).
cnf(c_139,plain,
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) ),
inference(clausify,[status(thm)],[cls_add__less__cancel__right_1]) ).
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_149,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_151,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]) ).
cnf(c_226,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A,
inference(resolve,[status(thm)],[c_151,c_149]) ).
cnf(c_237,plain,
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))) ),
inference(resolve,[status(thm)],[c_139,c_132]) ).
fof(cls_gr0__conv__Suc_1,axiom,
! [VAR_0] : hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Suc(VAR_0))),
file('theBenchmark.p',cls_gr0__conv__Suc_1) ).
cnf(c_269,plain,
hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Suc(A))),
inference(clausify,[status(thm)],[cls_gr0__conv__Suc_1]) ).
fof(cls_rangeI_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : hBOOL(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_500,plain,
hBOOL(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_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_710,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_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_745,plain,
( c_Finite__Set_Ofinite(B,A)
| ~ class_Finite__Set_Ofinite_Ofinite(A) ),
inference(clausify,[status(thm)],[cls_finite_0]) ).
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_778,plain,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
inference(clausify,[status(thm)],[clsarity_bool__Finite__Set_Ofinite_Ofinite]) ).
cnf(c_790,plain,
( ~ c_Finite__Set_Ofinite(B,tc_nat)
| ~ hBOOL(c_in(A,B,tc_nat))
| hBOOL(hAPP(c_lessequals(A,tc_nat),c_Finite__Set_Olinorder__class_OMax(B,tc_nat))) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_813,plain,
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),A))
| ~ hBOOL(hAPP(c_lessequals(A,tc_nat),B)) ),
inference(resolve,[status(thm)],[c_1,c_24]) ).
cnf(c_7166,plain,
hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(B)),A))),
inference(resolve,[status(thm)],[c_269,c_237]) ).
cnf(c_987,plain,
hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(B)),A))),
inference(paramod,[status(thm)],[c_226,c_7166]) ).
cnf(c_3391,plain,
c_Finite__Set_Ofinite(A,tc_bool),
inference(resolve,[status(thm)],[c_778,c_745]) ).
cnf(c_5138,plain,
c_Finite__Set_Ofinite(c_Set_Oimage(A,B,tc_bool,C),C),
inference(resolve,[status(thm)],[c_3391,c_710]) ).
cnf(c_6379,plain,
~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(A)),B),tc_nat),B)),
inference(resolve,[status(thm)],[c_987,c_813]) ).
cnf(c_7167,plain,
( ~ c_Finite__Set_Ofinite(c_Set_Oimage(A,c_Orderings_Otop__class_Otop(tc_fun(C,tc_bool)),C,tc_nat),tc_nat)
| hBOOL(hAPP(c_lessequals(hAPP(A,B),tc_nat),c_Finite__Set_Olinorder__class_OMax(c_Set_Oimage(A,c_Orderings_Otop__class_Otop(tc_fun(C,tc_bool)),C,tc_nat),tc_nat))) ),
inference(resolve,[status(thm)],[c_790,c_500]) ).
cnf(c_7164,plain,
hBOOL(hAPP(c_lessequals(hAPP(A,B),tc_nat),c_Finite__Set_Olinorder__class_OMax(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_7167,c_5138]) ).
cnf(c_7165,plain,
$false,
inference(resolve,[status(thm)],[c_7164,c_6379]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV876-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n008.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 15:06:39 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 3925426 was started by sandbox2 on n008,
% 0.11/0.37 % Sat Sep 26 15:06:39 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.42
% 0.15/0.42 % From the command line: assign(max_seconds, 300).
% 236.39/31.60
% 236.39/31.60 % given #500 (I,wt=9): 824 hBOOL(hAPP(c_lessequals(A,tc_nat),c_Orderings_Oord__class_Omax(A,B,tc_nat))). [resolve(1,a,44,a)].
% 236.39/31.60
% 236.39/31.60 % SZS status Unsatisfiable for theBenchmark
% 236.39/31.60
% 236.39/31.60 % Proof 1 at 5.42 (+ 1.15) seconds.
% 236.39/31.60 % Length of proof is 22.
% 236.39/31.60 % Level of proof is 4.
% 236.39/31.60 % Maximum clause weight is 28.000.
% 236.39/31.60 % Given clauses 694.
% 236.39/31.60
% 236.39/31.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------