%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL767-1 : 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 : n026.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 07:59:41 AM UTC 2026
% Result : Unsatisfiable 60.80s 9.22s
% Output : CNFRefutation 60.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 23 unt; 0 def)
% Number of atoms : 35 ( 26 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 13 ~; 6 |; 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 : 7 ( 7 usr; 1 con; 0-5 aty)
% Number of variables : 79 ( 21 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
cnf(c_31,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(clausify,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring__1]) ).
fof(cls_class__semiring_Osemiring__rules_I5_J_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_Ring__and__Field_Ocomm__semiring__1(VAR_0) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
cnf(c_32,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B
| ~ class_Ring__and__Field_Ocomm__semiring__1(A) ),
inference(clausify,[status(thm)],[cls_class__semiring_Osemiring__rules_I5_J_0]) ).
fof(cls_class__semiring_Osemiring__rules_I6_J_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_Ring__and__Field_Ocomm__semiring__1(VAR_0) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
cnf(c_33,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B
| ~ class_Ring__and__Field_Ocomm__semiring__1(A) ),
inference(clausify,[status(thm)],[cls_class__semiring_Osemiring__rules_I6_J_0]) ).
fof(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),VAR_1),VAR_2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),VAR_2),VAR_1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(VAR_0) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
cnf(c_41,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B)
| ~ class_Ring__and__Field_Ocomm__semiring__1(A) ),
inference(clausify,[status(thm)],[cls_class__semiring_Osemiring__rules_I24_J_0]) ).
cnf(c_60,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A),
inference(resolve,[status(thm)],[c_31,c_41]) ).
cnf(c_66,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A,
inference(resolve,[status(thm)],[c_31,c_33]) ).
cnf(c_67,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A,
inference(resolve,[status(thm)],[c_31,c_32]) ).
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_76,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_78,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_add__Suc__right_0,axiom,
! [VAR_0,VAR_1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),VAR_0),c_Suc(VAR_1)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),VAR_0),VAR_1)),
file('theBenchmark.p',cls_add__Suc__right_0) ).
cnf(c_362,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),
inference(clausify,[status(thm)],[cls_add__Suc__right_0]) ).
cnf(c_363,plain,
c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B)),
inference(copy,[status(thm)],[c_362]) ).
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_429,plain,
A != c_Suc(A),
inference(clausify,[status(thm)],[cls_n__not__Suc__n_0]) ).
cnf(c_430,plain,
c_Suc(A) != A,
inference(copy,[status(thm)],[c_429]) ).
cnf(c_553,plain,
hAPP(c_COMBB(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B,C,D,E),F) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(B,F)),A),
inference(paramod,[status(thm)],[c_76,c_60]) ).
cnf(c_576,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_67,c_78]) ).
cnf(c_898,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),
inference(paramod,[status(thm)],[c_363,c_430]) ).
cnf(c_1889,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) != A,
inference(paramod,[status(thm)],[c_66,c_898]) ).
cnf(c_1957,plain,
hAPP(c_COMBB(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),A,B,C,D),E) != hAPP(A,E),
inference(paramod,[status(thm)],[c_553,c_1889]) ).
cnf(c_2439,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_67,c_576]) ).
cnf(c_2441,plain,
hAPP(A,E) != hAPP(c_COMBB(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),A,B,C,D),E),
inference(copy,[status(thm)],[c_1957]) ).
cnf(c_2440,plain,
$false,
inference(resolve,[status(thm)],[c_2439,c_2441]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL767-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.44 % Computer : n026.cluster.edu
% 0.15/0.44 % Model : x86_64 x86_64
% 0.15/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.44 % Memory : 8046.5625MB
% 0.15/0.44 % OS : Linux 6.8.0-71-generic
% 0.15/0.44 % CPULimit : 300
% 0.15/0.44 % WCLimit : 300
% 0.15/0.44 % DateTime : Fri Sep 25 23:34:40 UTC 2026
% 0.15/0.44 % CPUTime :
% 0.15/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.44 % Process 3734403 was started by sandbox on n026,
% 0.15/0.44 % Fri Sep 25 23:34:40 2026
% 0.15/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.47
% 0.15/0.47 % From the command line: assign(max_seconds, 300).
% 60.80/9.22
% 60.80/9.22 % given #500 (T,wt=18): 1240 -c_Type_Otyping(A,B,C) | c_Type_Otyping(A,c_Lambda_Osubst(c_Lambda_OdB_OVar(D),B,D),C). [resolve(963,a,296,b)].
% 60.80/9.22
% 60.80/9.22 % SZS status Unsatisfiable for theBenchmark
% 60.80/9.22
% 60.80/9.22 % Proof 1 at 0.50 (+ 0.13) seconds.
% 60.80/9.22 % Length of proof is 20.
% 60.80/9.22 % Level of proof is 5.
% 60.80/9.22 % Maximum clause weight is 30.000.
% 60.80/9.22 % Given clauses 528.
% 60.80/9.22
% 60.80/9.22 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------