%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT079-1 : 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 08:28:28 AM UTC 2026
% Result : Unsatisfiable 63.80s 13.73s
% Output : CNFRefutation 63.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 53 ( 31 unt; 0 def)
% Number of atoms : 75 ( 56 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 52 ( 30 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-5 aty)
% Number of variables : 133 ( 41 sgn 34 !; 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_70,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_72,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_73,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_I22_J_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),VAR_1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),VAR_2),VAR_3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),VAR_2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),VAR_1),VAR_3))
| ~ class_Ring__and__Field_Ocomm__semiring__1(VAR_0) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
cnf(c_81,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))
| ~ class_Ring__and__Field_Ocomm__semiring__1(A) ),
inference(clausify,[status(thm)],[cls_class__semiring_Osemiring__rules_I22_J_0]) ).
fof(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
cnf(c_105,plain,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
inference(clausify,[status(thm)],[clsarity_nat__Ring__and__Field_Ozero__neq__one]) ).
fof(cls_zero__neq__one_0,axiom,
! [VAR_0] :
( c_HOL_Ozero__class_Ozero(VAR_0) != c_HOL_Oone__class_Oone(VAR_0)
| ~ class_Ring__and__Field_Ozero__neq__one(VAR_0) ),
file('theBenchmark.p',cls_zero__neq__one_0) ).
cnf(c_109,plain,
( c_HOL_Ozero__class_Ozero(A) != c_HOL_Oone__class_Oone(A)
| ~ class_Ring__and__Field_Ozero__neq__one(A) ),
inference(clausify,[status(thm)],[cls_zero__neq__one_0]) ).
fof(clsarity_nat__Ring__and__Field_Osemiring__1,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
cnf(c_113,plain,
class_Ring__and__Field_Osemiring__1(tc_nat),
inference(clausify,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring__1]) ).
fof(cls_of__nat__0_0,axiom,
! [VAR_0] :
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),VAR_0) = c_HOL_Ozero__class_Ozero(VAR_0)
| ~ class_Ring__and__Field_Osemiring__1(VAR_0) ),
file('theBenchmark.p',cls_of__nat__0_0) ).
cnf(c_115,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Ozero__class_Ozero(A)
| ~ class_Ring__and__Field_Osemiring__1(A) ),
inference(clausify,[status(thm)],[cls_of__nat__0_0]) ).
fof(cls_of__nat__Suc_0,axiom,
! [VAR_0,VAR_1] :
( c_Nat_Osemiring__1__class_Oof__nat(c_Suc(VAR_1),VAR_0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),c_HOL_Oone__class_Oone(VAR_0)),c_Nat_Osemiring__1__class_Oof__nat(VAR_1,VAR_0))
| ~ class_Ring__and__Field_Osemiring__1(VAR_0) ),
file('theBenchmark.p',cls_of__nat__Suc_0) ).
cnf(c_116,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A))
| ~ class_Ring__and__Field_Osemiring__1(A) ),
inference(clausify,[status(thm)],[cls_of__nat__Suc_0]) ).
cnf(c_159,plain,
c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),
inference(resolve,[status(thm)],[c_113,c_116]) ).
cnf(c_160,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)) = c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_nat),
inference(copy,[status(thm)],[c_159]) ).
cnf(c_161,plain,
c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(resolve,[status(thm)],[c_113,c_115]) ).
cnf(c_165,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat),
inference(resolve,[status(thm)],[c_105,c_109]) ).
cnf(c_186,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),
inference(resolve,[status(thm)],[c_70,c_81]) ).
cnf(c_192,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A,
inference(resolve,[status(thm)],[c_70,c_73]) ).
cnf(c_193,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A,
inference(resolve,[status(thm)],[c_70,c_72]) ).
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_204,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(c_COMBC(VAR_0,VAR_1,VAR_2,VAR_3),VAR_4),VAR_5) = hAPP(hAPP(VAR_0,VAR_5),VAR_4),
file('theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).
cnf(c_205,plain,
hAPP(hAPP(c_COMBC(A,B,C,D),E),F) = hAPP(hAPP(A,F),E),
inference(clausify,[status(thm)],[cls_ATP__Linkup_OCOMBC__def_0]) ).
fof(cls_add__is__0_0,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),VAR_0),VAR_1) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('theBenchmark.p',cls_add__is__0_0) ).
cnf(c_586,plain,
( A = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(clausify,[status(thm)],[cls_add__is__0_0]) ).
cnf(c_587,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = A
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(copy,[status(thm)],[c_586]) ).
fof(cls_natgb_Oadd__r0__iff_0,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = c_HOL_Ozero__class_Ozero(tc_nat)
| VAR_0 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),VAR_0),VAR_1) ),
file('theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
cnf(c_591,plain,
( B = c_HOL_Ozero__class_Ozero(tc_nat)
| A != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) ),
inference(clausify,[status(thm)],[cls_natgb_Oadd__r0__iff_0]) ).
cnf(c_19584,plain,
( B = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != A ),
inference(copy,[status(thm)],[c_591]) ).
cnf(c_592,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = B
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != A ),
inference(copy,[status(thm)],[c_19584]) ).
fof(cls_COMBS__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_COMBS__def_0) ).
cnf(c_657,plain,
hAPP(c_COMBS(A,B,C,D,E),F) = hAPP(hAPP(A,F),hAPP(B,F)),
inference(clausify,[status(thm)],[cls_COMBS__def_0]) ).
cnf(c_19585,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))),
inference(paramod,[status(thm)],[c_160,c_186]) ).
cnf(c_794,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),tc_nat)),
inference(copy,[status(thm)],[c_19585]) ).
cnf(c_862,plain,
hAPP(hAPP(c_COMBC(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A,B,C),D),E) = hAPP(E,D),
inference(paramod,[status(thm)],[c_193,c_205]) ).
cnf(c_867,plain,
hAPP(hAPP(c_COMBC(hAPP(c_COMBB(A,B,C),D),E,F,V6),V7),V8) = hAPP(D,hAPP(V8,V7)),
inference(paramod,[status(thm)],[c_205,c_204]) ).
cnf(c_19586,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
| c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramod,[status(thm)],[c_160,c_587]) ).
cnf(c_2650,plain,
c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(resolve,[status(thm)],[c_165,c_19586]) ).
cnf(c_19587,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))) != A ),
inference(paramod,[status(thm)],[c_794,c_592]) ).
cnf(c_19588,plain,
( c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))) != A ),
inference(copy,[status(thm)],[c_19587]) ).
cnf(c_6163,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))) != A,
inference(resolve,[status(thm)],[c_2650,c_19588]) ).
cnf(c_16432,plain,
hAPP(c_COMBS(c_COMBC(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A,B,C),D,E,F,V6),V7) = hAPP(hAPP(D,V7),V7),
inference(paramod,[status(thm)],[c_862,c_657]) ).
cnf(c_19589,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))) != A,
inference(paramod,[status(thm)],[c_161,c_6163]) ).
cnf(c_19142,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) != A,
inference(paramod,[status(thm)],[c_192,c_19589]) ).
cnf(c_19582,plain,
hAPP(hAPP(c_COMBC(hAPP(c_COMBB(A,B,C),hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat))),D,E,F),V6),V7) != hAPP(V7,V6),
inference(paramod,[status(thm)],[c_867,c_19142]) ).
cnf(c_19590,plain,
hAPP(hAPP(D,V7),V7) = hAPP(c_COMBS(c_COMBC(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A,B,C),D,E,F,V6),V7),
inference(copy,[status(thm)],[c_16432]) ).
cnf(c_19583,plain,
$false,
inference(resolve,[status(thm)],[c_19582,c_19590]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT079-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/5.45 % Computer : n026.cluster.edu
% 0.18/5.45 % Model : x86_64 x86_64
% 0.18/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.45 % Memory : 8046.5625MB
% 0.18/5.45 % OS : Linux 6.8.0-71-generic
% 0.18/5.45 % CPULimit : 300
% 0.18/5.45 % WCLimit : 300
% 0.18/5.45 % DateTime : Sat Sep 26 06:28:16 UTC 2026
% 0.18/5.45 % CPUTime :
% 0.18/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/5.45 % Process 307419 was started by sandbox on n026,
% 0.18/5.45 % Sat Sep 26 06:28:16 2026
% 0.18/5.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.22/5.51
% 0.22/5.51 % From the command line: assign(max_seconds, 300).
% 63.80/13.73
% 63.80/13.73 % given #500 (F,wt=7): 914 -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),A),A)). [resolve(240,a,209,a)].
% 63.80/13.73
% 63.80/13.73 % given #1000 (T,wt=10): 5322 class_Finite__Set_Ofinite_Ofinite(tc_fun(tc_prod(tc_fun(tc_bool,tc_bool),tc_bool),A)) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(4869,a,227,c)].
% 63.80/13.73
% 63.80/13.73 % SZS status Unsatisfiable for theBenchmark
% 63.80/13.73
% 63.80/13.73 % Proof 1 at 6.77 (+ 1.34) seconds.
% 63.80/13.73 % Length of proof is 32.
% 63.80/13.73 % Level of proof is 7.
% 63.80/13.73 % Maximum clause weight is 24.000.
% 63.80/13.73 % Given clauses 1175.
% 63.80/13.73
% 63.80/13.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------