%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV578-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 0.12s 0.71s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 11 unt; 0 def)
% Number of atoms : 25 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 24 ( 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1075,axiom,
! [T_a,V_f,V_m,V_n] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_m,tc_nat),V_n))
| c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_n,tc_nat),tc_nat,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(V_f,V_m)),c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_m),V_n,tc_nat),tc_nat,T_a))
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1079,axiom,
hBOOL(hAPP(c_HOL_Oord__class_Oless(v_m,tc_nat),v_n)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1080,axiom,
! [V_l,V_u] : c_SetInterval_Oord__class_OatLeastLessThan(hAPP(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(f1100,negated_conjecture,
class_OrderedGroup_Ocomm__monoid__add(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1101,negated_conjecture,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),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)) != 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(f3118,plain,
! [V_m,V_n] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(V_m,tc_nat),V_n))
| ! [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) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(V_f,V_m)),c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_m),V_n,tc_nat),tc_nat,T_a))
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ) ),
inference(miniscoping,[status(thm)],[f1075]) ).
fof(f3119,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X3))
| c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,tc_nat),tc_nat,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(X1,X2)),c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,X2),X3,tc_nat),tc_nat,X0))
| ~ class_OrderedGroup_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[status(thm)],[f3118]) ).
fof(f3124,plain,
hBOOL(hAPP(c_HOL_Oord__class_Oless(v_m,tc_nat),v_n)),
inference(cnf_transformation,[status(thm)],[f1079]) ).
fof(f3125,plain,
! [X0,X1] : c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,X0),X1,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(X0,X1,tc_nat),
inference(cnf_transformation,[status(thm)],[f1080]) ).
fof(f3164,plain,
class_OrderedGroup_Ocomm__monoid__add(t_a),
inference(cnf_transformation,[status(thm)],[f1100]) ).
fof(f3165,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),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)) != 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)],[f1101]) ).
fof(f3650,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X3))
| c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,tc_nat),tc_nat,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(X1,X2)),c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,tc_nat),tc_nat,X0))
| ~ class_OrderedGroup_Ocomm__monoid__add(X0) ),
inference(forward_demodulation,[status(thm)],[f3125,f3119]) ).
fof(f3653,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| c_Finite__Set_Osetsum(X0,c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,tc_nat),tc_nat,t_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(X0,X1)),c_Finite__Set_Osetsum(X0,c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,tc_nat),tc_nat,t_a)) ),
inference(resolution,[status(thm)],[f3650,f3164]) ).
fof(f3672,plain,
! [X0] : c_Finite__Set_Osetsum(X0,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(X0,v_m)),c_Finite__Set_Osetsum(X0,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a)),
inference(resolution,[status(thm)],[f3653,f3124]) ).
fof(f3677,plain,
c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),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(backward_demodulation,[status(thm)],[f3672,f3165]) ).
fof(f3687,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f3677]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV578-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.56 % Computer : n010.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Mon Sep 21 09:11:44 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.12/0.68 % Drodi V4.1.1
% 0.12/0.71 % Refutation found
% 0.12/0.71 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.78 % Elapsed time: 0.203167 seconds
% 0.12/0.78 % CPU time: 0.484887 seconds
% 0.12/0.78 % Total memory used: 158.389 MB
% 0.12/0.78 % Net memory used: 157.468 MB
%------------------------------------------------------------------------------