%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT089-1 : 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 : n013.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 08:28:29 AM UTC 2026
% Result : Unsatisfiable 40.45s 26.30s
% Output : CNFRefutation 40.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 23 unt; 0 def)
% Number of atoms : 27 ( 22 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 11 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-5 aty)
% Number of variables : 94 ( 39 sgn 16 !; 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_166,plain,
class_OrderedGroup_Omonoid__add(tc_nat),
inference(clausify,[status(thm)],[clsarity_nat__OrderedGroup_Omonoid__add]) ).
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_168,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_187,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A,
inference(resolve,[status(thm)],[c_166,c_168]) ).
fof(cls_ATP__Linkup_OCOMBB__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(hAPP(c_COMBB(VAR_0,VAR_1,VAR_2,VAR_3),VAR_4),VAR_5) = hAPP(VAR_0,hAPP(VAR_4,VAR_5)),
file('theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
cnf(c_271,plain,
hAPP(hAPP(c_COMBB(A,B,C,D),E),F) = hAPP(A,hAPP(E,F)),
inference(clausify,[status(thm)],[cls_ATP__Linkup_OCOMBB__def_0]) ).
fof(cls_ATP__Linkup_OCOMBS__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(c_COMBS(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4),VAR_5) = hAPP(hAPP(VAR_0,VAR_5),hAPP(VAR_1,VAR_5)),
file('theBenchmark.p',cls_ATP__Linkup_OCOMBS__def_0) ).
cnf(c_273,plain,
hAPP(c_COMBS(A,B,C,D,E),F) = hAPP(hAPP(A,F),hAPP(B,F)),
inference(clausify,[status(thm)],[cls_ATP__Linkup_OCOMBS__def_0]) ).
fof(cls_n__not__Suc__n_0,axiom,
! [VAR_0] : VAR_0 != c_Suc(VAR_0),
file('theBenchmark.p',cls_n__not__Suc__n_0) ).
cnf(c_425,plain,
A != c_Suc(A),
inference(clausify,[status(thm)],[cls_n__not__Suc__n_0]) ).
cnf(c_426,plain,
c_Suc(A) != A,
inference(copy,[status(thm)],[c_425]) ).
fof(cls_Suc__eq__plus1__left_0,axiom,
! [VAR_0] : c_Suc(VAR_0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),VAR_0),
file('theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
cnf(c_739,plain,
c_Suc(A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A),
inference(clausify,[status(thm)],[cls_Suc__eq__plus1__left_0]) ).
cnf(c_897,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) != A,
inference(paramod,[status(thm)],[c_739,c_426]) ).
cnf(c_1014,plain,
hAPP(c_COMBS(A,hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B,C,D),E) = hAPP(hAPP(A,E),E),
inference(paramod,[status(thm)],[c_187,c_273]) ).
cnf(c_20938,plain,
hAPP(hAPP(c_COMBB(A,B,C,D),c_COMBS(E,F,V6,V7,V8)),V9) = hAPP(A,hAPP(hAPP(E,V9),hAPP(F,V9))),
inference(paramod,[status(thm)],[c_273,c_271]) ).
cnf(c_1027,plain,
hAPP(A,hAPP(c_COMBS(B,C,D,E,F),V6)) = hAPP(A,hAPP(hAPP(B,V6),hAPP(C,V6))),
inference(paramod,[status(thm)],[c_271,c_20938]) ).
cnf(c_20939,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(A,B),hAPP(C,B))) != hAPP(c_COMBS(A,C,D,E,F),B),
inference(paramod,[status(thm)],[c_1027,c_897]) ).
cnf(c_18511,plain,
hAPP(c_COMBS(A,B,C,D,E),F) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(A,F),hAPP(B,F))),
inference(copy,[status(thm)],[c_20939]) ).
cnf(c_20817,plain,
hAPP(c_COMBS(A,B,C,D,E),F) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(c_COMBS(A,B,V6,V7,V8),F)),
inference(paramod,[status(thm)],[c_273,c_18511]) ).
cnf(c_20940,plain,
hAPP(hAPP(A,B),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(c_COMBS(A,hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C,D,E),B)),
inference(paramod,[status(thm)],[c_1014,c_20817]) ).
cnf(c_20936,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(c_COMBS(A,hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B,C,D),E)) != hAPP(hAPP(A,E),E),
inference(copy,[status(thm)],[c_20940]) ).
cnf(c_20941,plain,
hAPP(A,hAPP(E,F)) = hAPP(hAPP(c_COMBB(A,B,C,D),E),F),
inference(copy,[status(thm)],[c_271]) ).
cnf(c_20937,plain,
$false,
inference(resolve,[status(thm)],[c_20936,c_20941]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT089-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/20.40 % Computer : n013.cluster.edu
% 0.11/20.40 % Model : x86_64 x86_64
% 0.11/20.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/20.40 % Memory : 8046.5625MB
% 0.11/20.40 % OS : Linux 6.8.0-71-generic
% 0.11/20.40 % CPULimit : 300
% 0.11/20.40 % WCLimit : 300
% 0.11/20.40 % DateTime : Sat Sep 26 06:26:33 UTC 2026
% 0.11/20.41 % CPUTime :
% 0.11/20.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/20.41 % Process 2121822 was started by sandbox2 on n013,
% 0.11/20.41 % Sat Sep 26 06:26:33 2026
% 0.11/20.41 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/20.44
% 0.11/20.44 % From the command line: assign(max_seconds, 300).
% 40.45/26.30
% 40.45/26.30 % given #500 (I,wt=39): 868 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != c_HOL_Oone__class_Oone(tc_nat) | c_HOL_Ozero__class_Ozero(tc_nat) = A | c_HOL_Ozero__class_Ozero(tc_nat) = B. [back_rewrite(386),rewrite([739(7),188(12)])].
% 40.45/26.30
% 40.45/26.30 % given #1000 (A,wt=57): 955 hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Power_Opower__class_Opower(A,B,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | c_HOL_Oone__class_Oone(tc_nat) = A | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))). [resolve(241,c,199,c)].
% 40.45/26.30
% 40.45/26.30 % given #1500 (T,wt=27): 15134 c_HOL_Ozero__class_Ozero(tc_nat) = A | c_Lattices_Olower__semilattice__class_Oinf(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(2354,b,824,b)].
% 40.45/26.30
% 40.45/26.30 % given #2000 (W,wt=34): 20320 c_Lattices_Olower__semilattice__class_Oinf(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = A | c_Power_Opower__class_Opower(A,B,tc_nat) != c_Power_Opower__class_Opower(A,C,tc_nat) | B = C. [resolve(2781,b,263,b)].
% 40.45/26.30
% 40.45/26.30 % SZS status Unsatisfiable for theBenchmark
% 40.45/26.30
% 40.45/26.30 % Proof 1 at 4.68 (+ 1.06) seconds.
% 40.45/26.30 % Length of proof is 15.
% 40.45/26.30 % Level of proof is 6.
% 40.45/26.30 % Maximum clause weight is 60.000.
% 40.45/26.30 % Given clauses 2071.
% 40.45/26.30
% 40.45/26.30 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------