%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV578-1 : 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 : n005.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 24.59s 3.63s
% Output : CNFRefutation 24.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 12 unt; 0 def)
% Number of atoms : 22 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 9 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 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 : 21 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(tfree_tcs,axiom,
class_OrderedGroup_Ocomm__monoid__add(t_a),
file('theBenchmark.p',tfree_tcs) ).
cnf(c_352,plain,
class_OrderedGroup_Ocomm__monoid__add(t_a),
inference(clausify,[status(thm)],[tfree_tcs]) ).
fof(cls_setsum__head__upt__Suc_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(VAR_2,tc_nat),VAR_3))
| c_Finite__Set_Osetsum(VAR_1,c_SetInterval_Oord__class_OatLeastLessThan(VAR_2,VAR_3,tc_nat),tc_nat,VAR_0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),hAPP(VAR_1,VAR_2)),c_Finite__Set_Osetsum(VAR_1,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,VAR_2),VAR_3,tc_nat),tc_nat,VAR_0))
| ~ class_OrderedGroup_Ocomm__monoid__add(VAR_0) ),
file('theBenchmark.p',cls_setsum__head__upt__Suc_0) ).
cnf(c_359,plain,
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),D))
| c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat),tc_nat,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,C)),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,C),D,tc_nat),tc_nat,A))
| ~ class_OrderedGroup_Ocomm__monoid__add(A) ),
inference(clausify,[status(thm)],[cls_setsum__head__upt__Suc_0]) ).
fof(cls_less_0,axiom,
hBOOL(hAPP(c_HOL_Oord__class_Oless(v_m,tc_nat),v_n)),
file('theBenchmark.p',cls_less_0) ).
cnf(c_1420,plain,
hBOOL(hAPP(c_HOL_Oord__class_Oless(v_m,tc_nat),v_n)),
inference(clausify,[status(thm)],[cls_less_0]) ).
fof(cls_atLeastSucLessThan__greaterThanLessThan_0,axiom,
! [VAR_0,VAR_1] : c_SetInterval_Oord__class_OatLeastLessThan(hAPP(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_1421,plain,
c_SetInterval_Oord__class_OatLeastLessThan(hAPP(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_1422,plain,
c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,tc_nat) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,A),B,tc_nat),
inference(copy,[status(thm)],[c_1421]) ).
fof(cls_conjecture_0,axiom,
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('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1425,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(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_1716,plain,
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C))
| c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_nat,t_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(A,B)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),C,tc_nat),tc_nat,t_a)) ),
inference(resolve,[status(thm)],[c_352,c_359]) ).
cnf(c_1717,plain,
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(A,B)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),C,tc_nat),tc_nat,t_a)) = c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_nat,t_a) ),
inference(copy,[status(thm)],[c_1716]) ).
cnf(c_5379,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_OatLeastLessThan(hAPP(c_Suc,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(paramod,[status(thm)],[c_1422,c_1425]) ).
cnf(c_9260,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(A,v_m)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,v_m),v_n,tc_nat),tc_nat,t_a)) = c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a),
inference(resolve,[status(thm)],[c_1717,c_1420]) ).
cnf(c_9261,plain,
$false,
inference(resolve,[status(thm)],[c_9260,c_5379]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV578-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 14:31:47 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2354675 was started by sandbox2 on n005,
% 0.09/0.36 % Sat Sep 26 14:31:47 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.41
% 0.09/0.41 % From the command line: assign(max_seconds, 300).
% 24.59/3.63
% 24.59/3.63 % given #500 (I,wt=33): 1369 hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)) # tptp_name(cls_le__trans_0) # clausal_fof(1). [assumption].
% 24.59/3.63
% 24.59/3.63 % SZS status Unsatisfiable for theBenchmark
% 24.59/3.63
% 24.59/3.63 % Proof 1 at 2.92 (+ 0.21) seconds.
% 24.59/3.63 % Length of proof is 11.
% 24.59/3.63 % Level of proof is 4.
% 24.59/3.63 % Maximum clause weight is 61.000.
% 24.59/3.63 % Given clauses 759.
% 24.59/3.63
% 24.59/3.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------