%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV877-1 : 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 : n016.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 53.81s 20.82s
% Output : CNFRefutation 53.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of formulae : 30 ( 16 unt; 0 def)
% Number of atoms : 49 ( 3 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 23 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-4 aty)
% Number of variables : 65 ( 13 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_sup__ge1_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_lessequals(VAR_1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(VAR_0),VAR_1),VAR_2),VAR_0)
| ~ class_Lattices_Oupper__semilattice(VAR_0) ),
file('theBenchmark.p',cls_sup__ge1_0) ).
cnf(c_5,plain,
( c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),A)
| ~ class_Lattices_Oupper__semilattice(A) ),
inference(clausify,[status(thm)],[cls_sup__ge1_0]) ).
fof(cls_sup__left__commute_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(VAR_0),VAR_1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(VAR_0),VAR_2),VAR_3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(VAR_0),VAR_2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(VAR_0),VAR_1),VAR_3))
| ~ class_Lattices_Oupper__semilattice(VAR_0) ),
file('theBenchmark.p',cls_sup__left__commute_0) ).
cnf(c_21,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),D))
| ~ class_Lattices_Oupper__semilattice(A) ),
inference(clausify,[status(thm)],[cls_sup__left__commute_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_160,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),C)),
inference(resolve,[status(thm)],[c_24,c_21]) ).
cnf(c_174,plain,
c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B),tc_nat),
inference(resolve,[status(thm)],[c_24,c_5]) ).
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_230,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_256,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_399,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_481,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_523,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_1162,plain,
c_Finite__Set_Ofinite(A,tc_bool),
inference(resolve,[status(thm)],[c_230,c_202]) ).
cnf(c_2073,plain,
~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),c_Suc(A)),B),A,tc_nat),
inference(resolve,[status(thm)],[c_523,c_174]) ).
cnf(c_7392,plain,
c_Finite__Set_Ofinite(c_Set_Oimage(A,B,tc_bool,C),C),
inference(resolve,[status(thm)],[c_1162,c_256]) ).
cnf(c_8306,plain,
~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),c_Suc(B)),C)),B,tc_nat),
inference(paramod,[status(thm)],[c_160,c_2073]) ).
cnf(c_10693,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_481,c_210]) ).
cnf(c_10694,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_10693,c_399]) ).
cnf(c_10691,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_10694,c_7392]) ).
cnf(c_10692,plain,
$false,
inference(resolve,[status(thm)],[c_10691,c_8306]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV877-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.56 % Computer : n016.cluster.edu
% 0.10/5.56 % Model : x86_64 x86_64
% 0.10/5.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.56 % Memory : 8046.5625MB
% 0.10/5.56 % OS : Linux 6.8.0-71-generic
% 0.10/5.56 % CPULimit : 300
% 0.10/5.56 % WCLimit : 300
% 0.10/5.56 % DateTime : Sat Sep 26 15:11:06 UTC 2026
% 0.10/5.56 % CPUTime :
% 0.10/5.56 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.56 % Process 1164331 was started by sandbox on n016,
% 0.10/5.56 % Sat Sep 26 15:11:06 2026
% 0.10/5.56 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.58
% 0.10/5.58 % From the command line: assign(max_seconds, 300).
% 53.81/20.82
% 53.81/20.82 % given #500 (I,wt=14): 718 c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat) # tptp_name(cls_Suc__mono_0) # clausal_fof(1). [assumption].
% 53.81/20.82
% 53.81/20.82 % SZS status Unsatisfiable for theBenchmark
% 53.81/20.82
% 53.81/20.82 % Proof 1 at 2.86 (+ 0.51) seconds.
% 53.81/20.82 % Length of proof is 18.
% 53.81/20.82 % Level of proof is 4.
% 53.81/20.82 % Maximum clause weight is 45.000.
% 53.81/20.82 % Given clauses 763.
% 53.81/20.82
% 53.81/20.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------