%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV578-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:27:00 PM UTC 2026
% Result : Unsatisfiable 3.83s 3.28s
% Output : CNFRefutation 3.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 12 ( 10 unt; 0 nHn; 8 RR)
% Number of literals : 16 ( 7 equ; 7 neg)
% Maximal clause size : 3 ( 1 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 : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,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',cls_conjecture_0) ).
cnf(cls_atLeastSucLessThan__greaterThanLessThan_0,axiom,
c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,X1),X2,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastSucLessThan__greaterThanLessThan_0) ).
cnf(cls_setsum__head__upt__Suc_0,axiom,
( c_Finite__Set_Osetsum(X2,c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,tc_nat),tc_nat,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(X2,X3)),c_Finite__Set_Osetsum(X2,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,X3),X4,tc_nat),tc_nat,X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__head__upt__Suc_0) ).
cnf(tfree_tcs,negated_conjecture,
class_OrderedGroup_Ocomm__monoid__add(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(cls_less_0,axiom,
hBOOL(hAPP(c_HOL_Oord__class_Oless(v_m,tc_nat),v_n)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less_0) ).
cnf(c_0_5,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),
cls_conjecture_0 ).
cnf(c_0_6,axiom,
c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,X1),X2,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,tc_nat),
cls_atLeastSucLessThan__greaterThanLessThan_0 ).
cnf(c_0_7,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_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(rw,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,axiom,
( c_Finite__Set_Osetsum(X2,c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,tc_nat),tc_nat,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(X2,X3)),c_Finite__Set_Osetsum(X2,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,X3),X4,tc_nat),tc_nat,X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),X4)) ),
cls_setsum__head__upt__Suc_0 ).
cnf(c_0_9,negated_conjecture,
class_OrderedGroup_Ocomm__monoid__add(t_a),
tfree_tcs ).
cnf(c_0_10,axiom,
hBOOL(hAPP(c_HOL_Oord__class_Oless(v_m,tc_nat),v_n)),
cls_less_0 ).
cnf(c_0_11,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV578-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.17/0.33 % Computer : n019.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 05:36:14 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 3.83/3.28 % Version : CSE_E---1.7
% 3.83/3.28 % Problem : theBenchmark.p
% 3.83/3.28 % SZS status Unsatisfiable for theBenchmark.p
% 3.83/3.28 % SZS output start CNFRefutation
% See solution above
% 3.83/3.29 % Total time : 2.486s
%------------------------------------------------------------------------------