%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV685-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 09:08:56 AM UTC 2026
% Result : Unsatisfiable 36.74s 5.72s
% Output : CNFRefutation 36.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 19 unt; 0 def)
% Number of atoms : 48 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 22 ~; 16 |; 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 : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 107 ( 33 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
cnf(c_200,plain,
class_OrderedGroup_Omonoid__add(tc_nat),
inference(clausify,[status(thm)],[clsarity_nat__OrderedGroup_Omonoid__add]) ).
fof(cls_monoid__add__class_Oadd__0__right_0,axiom,
! [VAR_0,VAR_1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),VAR_1),c_HOL_Ozero__class_Ozero(VAR_0)) = VAR_1
| ~ class_OrderedGroup_Omonoid__add(VAR_0) ),
file('theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
cnf(c_201,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B
| ~ class_OrderedGroup_Omonoid__add(A) ),
inference(clausify,[status(thm)],[cls_monoid__add__class_Oadd__0__right_0]) ).
fof(cls_add__0__left_0,axiom,
! [VAR_0,VAR_1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),c_HOL_Ozero__class_Ozero(VAR_0)),VAR_1) = VAR_1
| ~ class_OrderedGroup_Omonoid__add(VAR_0) ),
file('theBenchmark.p',cls_add__0__left_0) ).
cnf(c_202,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B
| ~ class_OrderedGroup_Omonoid__add(A) ),
inference(clausify,[status(thm)],[cls_add__0__left_0]) ).
cnf(c_361,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A,
inference(resolve,[status(thm)],[c_200,c_202]) ).
cnf(c_362,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A,
inference(resolve,[status(thm)],[c_200,c_201]) ).
fof(cls_ATP__Linkup_OCOMBB__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(hAPP(hAPP(c_COMBB(VAR_0,VAR_1,VAR_2),VAR_3),VAR_4),VAR_5) = hAPP(VAR_3,hAPP(VAR_4,VAR_5)),
file('theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
cnf(c_449,plain,
hAPP(hAPP(hAPP(c_COMBB(A,B,C),D),E),F) = hAPP(D,hAPP(E,F)),
inference(clausify,[status(thm)],[cls_ATP__Linkup_OCOMBB__def_0]) ).
fof(cls_ATP__Linkup_OCOMBC__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(hAPP(hAPP(c_COMBC(VAR_0,VAR_1,VAR_2),VAR_3),VAR_4),VAR_5) = hAPP(hAPP(VAR_3,VAR_5),VAR_4),
file('theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).
cnf(c_450,plain,
hAPP(hAPP(hAPP(c_COMBC(A,B,C),D),E),F) = hAPP(hAPP(D,F),E),
inference(clausify,[status(thm)],[cls_ATP__Linkup_OCOMBC__def_0]) ).
fof(cls_ATP__Linkup_OCOMBS__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(hAPP(hAPP(c_COMBS(VAR_0,VAR_1,VAR_2),VAR_3),VAR_4),VAR_5) = hAPP(hAPP(VAR_3,VAR_5),hAPP(VAR_4,VAR_5)),
file('theBenchmark.p',cls_ATP__Linkup_OCOMBS__def_0) ).
cnf(c_451,plain,
hAPP(hAPP(hAPP(c_COMBS(A,B,C),D),E),F) = hAPP(hAPP(D,F),hAPP(E,F)),
inference(clausify,[status(thm)],[cls_ATP__Linkup_OCOMBS__def_0]) ).
fof(cls_not__add__less2_0,axiom,
! [VAR_0,VAR_1] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),VAR_0),VAR_1),VAR_1,tc_nat),
file('theBenchmark.p',cls_not__add__less2_0) ).
cnf(c_502,plain,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat),
inference(clausify,[status(thm)],[cls_not__add__less2_0]) ).
fof(cls_less__add__eq__less_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_HOL_Oord__class_Oless(VAR_0,VAR_3,tc_nat)
| ~ c_HOL_Oord__class_Oless(VAR_2,VAR_1,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),VAR_0),VAR_1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),VAR_2),VAR_3) ),
file('theBenchmark.p',cls_less__add__eq__less_0) ).
cnf(c_519,plain,
( c_HOL_Oord__class_Oless(A,D,tc_nat)
| ~ c_HOL_Oord__class_Oless(C,B,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D) ),
inference(clausify,[status(thm)],[cls_less__add__eq__less_0]) ).
fof(cls_not__less__eq_0,axiom,
! [VAR_0,VAR_1] :
( c_HOL_Oord__class_Oless(VAR_1,VAR_0,tc_nat)
| c_HOL_Oord__class_Oless(VAR_0,hAPP(c_Suc,VAR_1),tc_nat) ),
file('theBenchmark.p',cls_not__less__eq_0) ).
cnf(c_533,plain,
( c_HOL_Oord__class_Oless(B,A,tc_nat)
| c_HOL_Oord__class_Oless(A,hAPP(c_Suc,B),tc_nat) ),
inference(clausify,[status(thm)],[cls_not__less__eq_0]) ).
fof(cls_gr__implies__not0_0,axiom,
! [VAR_0] : ~ c_HOL_Oord__class_Oless(VAR_0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('theBenchmark.p',cls_gr__implies__not0_0) ).
cnf(c_635,plain,
~ c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(clausify,[status(thm)],[cls_gr__implies__not0_0]) ).
cnf(c_1018,plain,
hAPP(hAPP(hAPP(c_COMBC(A,B,C),hAPP(c_COMBB(D,E,F),V6)),V7),V8) = hAPP(V6,hAPP(V8,V7)),
inference(paramod,[status(thm)],[c_450,c_449]) ).
cnf(c_1207,plain,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(hAPP(c_COMBS(A,B,C),c_HOL_Oplus__class_Oplus(tc_nat)),D),E),hAPP(D,E),tc_nat),
inference(paramod,[status(thm)],[c_451,c_502]) ).
cnf(c_11596,plain,
( c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(C,B,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != C ),
inference(paramod,[status(thm)],[c_362,c_519]) ).
cnf(c_1248,plain,
( ~ c_HOL_Oord__class_Oless(C,B,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != C ),
inference(resolve,[status(thm)],[c_635,c_11596]) ).
cnf(c_3140,plain,
( ~ c_HOL_Oord__class_Oless(B,A,tc_nat)
| A != B ),
inference(paramod,[status(thm)],[c_361,c_1248]) ).
cnf(c_3202,plain,
( c_HOL_Oord__class_Oless(A,B,tc_nat)
| hAPP(c_Suc,A) != B ),
inference(resolve,[status(thm)],[c_3140,c_533]) ).
cnf(c_7098,plain,
~ c_HOL_Oord__class_Oless(hAPP(hAPP(hAPP(c_COMBS(A,B,C),c_HOL_Oplus__class_Oplus(tc_nat)),hAPP(hAPP(c_COMBS(D,E,F),V6),V7)),V8),hAPP(hAPP(V6,V8),hAPP(V7,V8)),tc_nat),
inference(paramod,[status(thm)],[c_451,c_1207]) ).
cnf(c_11597,plain,
( c_HOL_Oord__class_Oless(A,B,tc_nat)
| B != hAPP(c_Suc,A) ),
inference(copy,[status(thm)],[c_3202]) ).
cnf(c_11594,plain,
c_HOL_Oord__class_Oless(hAPP(A,B),hAPP(hAPP(hAPP(c_COMBC(C,D,E),hAPP(c_COMBB(F,V6,V7),c_Suc)),B),A),tc_nat),
inference(resolve,[status(thm)],[c_1018,c_11597]) ).
cnf(c_11595,plain,
$false,
inference(resolve,[status(thm)],[c_11594,c_7098]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV685-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 14:51:02 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 1124555 was started by sandbox on n016,
% 0.11/0.37 % Sat Sep 26 14:51:02 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.40
% 0.11/0.40 % From the command line: assign(max_seconds, 300).
% 36.74/5.72
% 36.74/5.72 % given #500 (W,wt=21): 4022 c_HOL_Oord__class_Oless(A,B,tc_nat) | A = B | c_HOL_Ozero__class_Ozero(tc_nat) != A. [resolve(2968,a,3140,b),flip(c)].
% 36.74/5.72
% 36.74/5.72 % SZS status Unsatisfiable for theBenchmark
% 36.74/5.72
% 36.74/5.72 % Proof 1 at 4.38 (+ 0.90) seconds.
% 36.74/5.72 % Length of proof is 20.
% 36.74/5.72 % Level of proof is 6.
% 36.74/5.72 % Maximum clause weight is 87.000.
% 36.74/5.72 % Given clauses 854.
% 36.74/5.72
% 36.74/5.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------