%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV580-1 : 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 : n004.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 4.08s 16.30s
% Output : CNFRefutation 4.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 43 ( 31 unt; 0 def)
% Number of atoms : 57 ( 36 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 20 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-4 aty)
% Number of variables : 45 ( 1 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_ivl__disj__un_I3_J_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_HOL_Oord__class_Oless(VAR_1,VAR_2,VAR_0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(VAR_1,c_Orderings_Obot__class_Obot(tc_fun(VAR_0,tc_bool)),VAR_0),c_SetInterval_Oord__class_OgreaterThanLessThan(VAR_1,VAR_2,VAR_0),tc_fun(VAR_0,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(VAR_1,VAR_2,VAR_0)
| ~ class_Orderings_Olinorder(VAR_0) ),
file('theBenchmark.p',cls_ivl__disj__un_I3_J_0) ).
cnf(c_37,plain,
( ~ c_HOL_Oord__class_Oless(B,C,A)
| c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),c_SetInterval_Oord__class_OgreaterThanLessThan(B,C,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(B,C,A)
| ~ class_Orderings_Olinorder(A) ),
inference(clausify,[status(thm)],[cls_ivl__disj__un_I3_J_0]) ).
fof(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
file('theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
cnf(c_38,plain,
class_Orderings_Olinorder(tc_nat),
inference(clausify,[status(thm)],[clsarity_nat__Orderings_Olinorder]) ).
cnf(c_196,plain,
( ~ c_HOL_Oord__class_Oless(A,B,tc_nat)
| c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat) ),
inference(resolve,[status(thm)],[c_37,c_38]) ).
fof(cls_Collect__def_0,axiom,
! [VAR_0,VAR_1] : c_Collect(VAR_0,VAR_1) = VAR_0,
file('theBenchmark.p',cls_Collect__def_0) ).
cnf(c_392,plain,
c_Collect(A,B) = A,
inference(clausify,[status(thm)],[cls_Collect__def_0]) ).
fof(cls_singleton__conv2_0,axiom,
! [VAR_0,VAR_1] : c_Collect(c_fequal(VAR_0,VAR_1),VAR_1) = c_Set_Oinsert(VAR_0,c_Orderings_Obot__class_Obot(tc_fun(VAR_1,tc_bool)),VAR_1),
file('theBenchmark.p',cls_singleton__conv2_0) ).
cnf(c_464,plain,
c_Collect(c_fequal(A,B),B) = c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),
inference(clausify,[status(thm)],[cls_singleton__conv2_0]) ).
cnf(c_2262,plain,
c_fequal(A,B) = c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),
inference(paramod,[status(thm)],[c_392,c_464]) ).
cnf(c_465,plain,
c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B) = c_fequal(A,B),
inference(copy,[status(thm)],[c_2262]) ).
fof(cls_less_0,axiom,
c_HOL_Oord__class_Oless(v_m,v_n,tc_nat),
file('theBenchmark.p',cls_less_0) ).
cnf(c_518,plain,
c_HOL_Oord__class_Oless(v_m,v_n,tc_nat),
inference(clausify,[status(thm)],[cls_less_0]) ).
fof(cls_atLeastSucLessThan__greaterThanLessThan_0,axiom,
! [VAR_0,VAR_1] : c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(VAR_0),VAR_1,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(VAR_0,VAR_1,tc_nat),
file('theBenchmark.p',cls_atLeastSucLessThan__greaterThanLessThan_0) ).
cnf(c_523,plain,
c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(A),B,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,tc_nat),
inference(clausify,[status(thm)],[cls_atLeastSucLessThan__greaterThanLessThan_0]) ).
cnf(c_524,plain,
c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,tc_nat) = c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(A),B,tc_nat),
inference(copy,[status(thm)],[c_523]) ).
fof(cls_calculation_0,axiom,
( c_HOL_Oplus__class_Oplus(hAPP(v_f,v_m),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a),t_a) = c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(t_a) ),
file('theBenchmark.p',cls_calculation_0) ).
cnf(c_532,plain,
( c_HOL_Oplus__class_Oplus(hAPP(v_f,v_m),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a),t_a) = c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(t_a) ),
inference(clausify,[status(thm)],[cls_calculation_0]) ).
cnf(c_2263,plain,
( c_HOL_Oplus__class_Oplus(hAPP(v_f,v_m),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(v_m),v_n,tc_nat),tc_nat,t_a),t_a) = c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(t_a) ),
inference(paramod,[status(thm)],[c_524,c_532]) ).
cnf(c_2264,plain,
( c_HOL_Oplus__class_Oplus(hAPP(v_f,v_m),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(v_m),v_n,tc_nat),tc_nat,t_a),t_a) = c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_fequal(v_m,tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(t_a) ),
inference(paramod,[status(thm)],[c_465,c_2263]) ).
cnf(c_2265,plain,
( c_HOL_Oplus__class_Oplus(hAPP(v_f,v_m),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(v_m),v_n,tc_nat),tc_nat,t_a),t_a) = c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_fequal(v_m,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(v_m),v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(t_a) ),
inference(paramod,[status(thm)],[c_524,c_2264]) ).
cnf(c_533,plain,
( c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_fequal(v_m,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(v_m),v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a) = c_HOL_Oplus__class_Oplus(hAPP(v_f,v_m),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(v_m),v_n,tc_nat),tc_nat,t_a),t_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(t_a) ),
inference(copy,[status(thm)],[c_2265]) ).
fof(cls_Un__empty__right_0,axiom,
! [VAR_0,VAR_1] : c_Lattices_Oupper__semilattice__class_Osup(VAR_0,c_Orderings_Obot__class_Obot(tc_fun(VAR_1,tc_bool)),tc_fun(VAR_1,tc_bool)) = VAR_0,
file('theBenchmark.p',cls_Un__empty__right_0) ).
cnf(c_558,plain,
c_Lattices_Oupper__semilattice__class_Osup(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),tc_fun(B,tc_bool)) = A,
inference(clausify,[status(thm)],[cls_Un__empty__right_0]) ).
fof(cls_insert__is__Un_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_Set_Oinsert(VAR_0,VAR_1,VAR_2) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(VAR_0,c_Orderings_Obot__class_Obot(tc_fun(VAR_2,tc_bool)),VAR_2),VAR_1,tc_fun(VAR_2,tc_bool)),
file('theBenchmark.p',cls_insert__is__Un_0) ).
cnf(c_581,plain,
c_Set_Oinsert(A,B,C) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),B,tc_fun(C,tc_bool)),
inference(clausify,[status(thm)],[cls_insert__is__Un_0]) ).
cnf(c_582,plain,
c_Set_Oinsert(A,B,C) = c_Lattices_Oupper__semilattice__class_Osup(c_fequal(A,C),B,tc_fun(C,tc_bool)),
inference(paramod,[status(thm)],[c_465,c_581]) ).
fof(tfree_tcs,axiom,
class_OrderedGroup_Ocomm__monoid__add(t_a),
file('theBenchmark.p',tfree_tcs) ).
cnf(c_585,plain,
class_OrderedGroup_Ocomm__monoid__add(t_a),
inference(clausify,[status(thm)],[tfree_tcs]) ).
fof(cls_conjecture_0,axiom,
c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a) != c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_586,plain,
c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a) != c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_2266,plain,
c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_fequal(v_m,tc_nat),c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a) != c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a),
inference(paramod,[status(thm)],[c_582,c_586]) ).
cnf(c_2267,plain,
c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_fequal(v_m,tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a) != c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a),
inference(paramod,[status(thm)],[c_558,c_2266]) ).
cnf(c_587,plain,
c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_fequal(v_m,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(v_m),v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a) != c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a),
inference(paramod,[status(thm)],[c_524,c_2267]) ).
cnf(c_2268,plain,
( ~ c_HOL_Oord__class_Oless(A,B,tc_nat)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_fequal(A,tc_nat),c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat) ),
inference(paramod,[status(thm)],[c_582,c_196]) ).
cnf(c_2269,plain,
( ~ c_HOL_Oord__class_Oless(A,B,tc_nat)
| c_Lattices_Oupper__semilattice__class_Osup(c_fequal(A,tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat) ),
inference(paramod,[status(thm)],[c_558,c_2268]) ).
cnf(c_790,plain,
( ~ c_HOL_Oord__class_Oless(A,B,tc_nat)
| c_Lattices_Oupper__semilattice__class_Osup(c_fequal(A,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(A),B,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat) ),
inference(paramod,[status(thm)],[c_524,c_2269]) ).
cnf(c_831,plain,
c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_fequal(v_m,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(v_m),v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a) = c_HOL_Oplus__class_Oplus(hAPP(v_f,v_m),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(v_m),v_n,tc_nat),tc_nat,t_a),t_a),
inference(resolve,[status(thm)],[c_585,c_533]) ).
cnf(c_840,plain,
c_HOL_Oplus__class_Oplus(hAPP(v_f,v_m),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(v_m),v_n,tc_nat),tc_nat,t_a),t_a) != c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a),
inference(paramod,[status(thm)],[c_831,c_587]) ).
cnf(c_2254,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_fequal(v_m,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(v_m),v_n,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),
inference(resolve,[status(thm)],[c_790,c_518]) ).
cnf(c_2270,plain,
c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a) = c_HOL_Oplus__class_Oplus(hAPP(v_f,v_m),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(v_m),v_n,tc_nat),tc_nat,t_a),t_a),
inference(paramod,[status(thm)],[c_2254,c_831]) ).
cnf(c_2271,plain,
c_HOL_Oplus__class_Oplus(hAPP(v_f,v_m),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(v_m),v_n,tc_nat),tc_nat,t_a),t_a) = c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a),
inference(copy,[status(thm)],[c_2270]) ).
cnf(c_2261,plain,
$false,
inference(resolve,[status(thm)],[c_840,c_2271]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV580-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/15.66 % Computer : n004.cluster.edu
% 0.16/15.66 % Model : x86_64 x86_64
% 0.16/15.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/15.66 % Memory : 8046.5625MB
% 0.16/15.66 % OS : Linux 6.8.0-71-generic
% 0.16/15.66 % CPULimit : 300
% 0.16/15.66 % WCLimit : 300
% 0.16/15.66 % DateTime : Sat Sep 26 14:32:27 UTC 2026
% 0.16/15.67 % CPUTime :
% 0.16/15.67 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/15.67 % Process 1946847 was started by sandbox2 on n004,
% 0.16/15.67 % Sat Sep 26 14:32:27 2026
% 0.16/15.67 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.20/15.70
% 0.20/15.70 % From the command line: assign(max_seconds, 300).
% 4.08/16.30
% 4.08/16.30 % SZS status Unsatisfiable for theBenchmark
% 4.08/16.30
% 4.08/16.30 % Proof 1 at 0.48 (+ 0.07) seconds.
% 4.08/16.30 % Length of proof is 22.
% 4.08/16.30 % Level of proof is 5.
% 4.08/16.30 % Maximum clause weight is 33.000.
% 4.08/16.30 % Given clauses 422.
% 4.08/16.30
% 4.08/16.30 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------