%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV580-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 : Thu Sep 24 02:49:10 PM UTC 2026
% Result : Unsatisfiable 0.28s 0.64s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 12 unt; 0 def)
% Number of atoms : 30 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 16 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-4 aty)
% Number of variables : 20 ( 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f187,axiom,
! [T_a,V_f,V_m,V_n] :
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| 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)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f499,axiom,
c_HOL_Oord__class_Oless(v_m,v_n,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f502,axiom,
! [V_l,V_u] : c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(V_l),V_u,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(V_l,V_u,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f508,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('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f553,negated_conjecture,
class_OrderedGroup_Ocomm__monoid__add(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f554,negated_conjecture,
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('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f902,plain,
! [V_m,V_n] :
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ! [T_a] :
( ! [V_f] : 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)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ) ),
inference(miniscoping,[status(thm)],[f187]) ).
fof(f903,plain,
! [X0,X1,X2,X3] :
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,tc_nat),tc_nat,X0) = c_HOL_Oplus__class_Oplus(hAPP(X1,X2),c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(X2),X3,tc_nat),tc_nat,X0),X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[status(thm)],[f902]) ).
fof(f1387,plain,
c_HOL_Oord__class_Oless(v_m,v_n,tc_nat),
inference(cnf_transformation,[status(thm)],[f499]) ).
fof(f1390,plain,
! [X0,X1] : c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(X0),X1,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(X0,X1,tc_nat),
inference(cnf_transformation,[status(thm)],[f502]) ).
fof(f1398,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(cnf_transformation,[status(thm)],[f508]) ).
fof(f1468,plain,
class_OrderedGroup_Ocomm__monoid__add(t_a),
inference(cnf_transformation,[status(thm)],[f553]) ).
fof(f1469,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(cnf_transformation,[status(thm)],[f554]) ).
fof(f1556,plain,
! [X0,X1,X2,X3] :
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,tc_nat),tc_nat,X0) = c_HOL_Oplus__class_Oplus(hAPP(X1,X2),c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,tc_nat),tc_nat,X0),X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0) ),
inference(forward_demodulation,[status(thm)],[f1390,f903]) ).
fof(f2869,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_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a),
inference(backward_demodulation,[status(thm)],[f2870,f1469]) ).
fof(f2870,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),
inference(forward_subsumption_resolution,[status(thm)],[f1398,f1468]) ).
fof(f3014,plain,
( ~ c_HOL_Oord__class_Oless(v_m,v_n,tc_nat)
| ~ class_OrderedGroup_Ocomm__monoid__add(t_a) ),
inference(resolution,[status(thm)],[f2869,f1556]) ).
fof(f3015,plain,
~ c_HOL_Oord__class_Oless(v_m,v_n,tc_nat),
inference(forward_subsumption_resolution,[status(thm)],[f3014,f1468]) ).
fof(f3016,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3015,f1387]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV580-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n011.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 09:11:40 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.28/0.51 % Drodi V4.1.1
% 0.28/0.64 % Refutation found
% 0.28/0.64 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.28/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.28/0.67 % Elapsed time: 0.219492 seconds
% 0.28/0.67 % CPU time: 1.050162 seconds
% 0.28/0.67 % Total memory used: 142.756 MB
% 0.28/0.67 % Net memory used: 142.284 MB
%------------------------------------------------------------------------------