%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV658-1 : 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 : 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 09:08:54 AM UTC 2026
% Result : Unsatisfiable 82.82s 11.93s
% Output : CNFRefutation 82.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 16 unt; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-5 aty)
% Number of variables : 76 ( 39 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_ATP__Linkup_OCOMBB__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(c_COMBB(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4),VAR_5) = hAPP(VAR_0,hAPP(VAR_1,VAR_5)),
file('theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
cnf(c_705,plain,
hAPP(c_COMBB(A,B,C,D,E),F) = hAPP(A,hAPP(B,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_708,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_plus__nat_Oadd__0_0,axiom,
! [VAR_0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),VAR_0) = VAR_0,
file('theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
cnf(c_738,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A,
inference(clausify,[status(thm)],[cls_plus__nat_Oadd__0_0]) ).
fof(cls_n__not__Suc__n_0,axiom,
! [VAR_0] : VAR_0 != hAPP(c_Suc,VAR_0),
file('theBenchmark.p',cls_n__not__Suc__n_0) ).
cnf(c_864,plain,
A != hAPP(c_Suc,A),
inference(clausify,[status(thm)],[cls_n__not__Suc__n_0]) ).
cnf(c_865,plain,
hAPP(c_Suc,A) != A,
inference(copy,[status(thm)],[c_864]) ).
cnf(c_1486,plain,
hAPP(c_COMBS(A,B,C,D,E),F) = hAPP(c_COMBS(A,B,V6,V7,V8),F),
inference(paramod,[status(thm)],[c_708,c_708]) ).
cnf(c_1495,plain,
hAPP(c_COMBS(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A,B,C,D),E) = hAPP(E,hAPP(A,E)),
inference(paramod,[status(thm)],[c_738,c_708]) ).
cnf(c_1624,plain,
hAPP(c_COMBB(c_Suc,A,B,C,D),E) != hAPP(A,E),
inference(paramod,[status(thm)],[c_705,c_865]) ).
cnf(c_6005,plain,
hAPP(c_COMBB(c_Suc,c_COMBS(A,B,C,D,E),F,V6,V7),V8) != hAPP(c_COMBS(A,B,V9,V10,V11),V8),
inference(paramod,[status(thm)],[c_1486,c_1624]) ).
cnf(c_5586,plain,
hAPP(c_COMBS(A,B,C,D,E),F) != hAPP(c_COMBB(c_Suc,c_COMBS(A,B,V6,V7,V8),V9,V10,V11),F),
inference(copy,[status(thm)],[c_6005]) ).
cnf(c_6003,plain,
hAPP(c_COMBS(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A,B,C),D) = hAPP(D,D),
inference(paramod,[status(thm)],[c_738,c_1495]) ).
cnf(c_6004,plain,
$false,
inference(resolve,[status(thm)],[c_6003,c_5586]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV658-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 14:41:21 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2965317 was started by sandbox on n013,
% 0.10/0.37 % Sat Sep 26 14:41:21 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.40
% 0.14/0.40 % From the command line: assign(max_seconds, 300).
% 82.82/11.93
% 82.82/11.93 % given #500 (I,wt=15): 1268 hAPP(c_Power_Opower__class_Opower(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat). [copy(1267),unit_del(a,733),unit_del(b,731),unit_del(c,727)].
% 82.82/11.93
% 82.82/11.93 % given #1000 (T,wt=19): 3344 c_lessequals(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | c_lessequals(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint). [resolve(3192,a,916,d),unit_del(b,721)].
% 82.82/11.93
% 82.82/11.93 % SZS status Unsatisfiable for theBenchmark
% 82.82/11.93
% 82.82/11.93 % Proof 1 at 2.87 (+ 0.56) seconds.
% 82.82/11.93 % Length of proof is 11.
% 82.82/11.93 % Level of proof is 4.
% 82.82/11.93 % Maximum clause weight is 30.000.
% 82.82/11.93 % Given clauses 1004.
% 82.82/11.93
% 82.82/11.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------