%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV668-1 : 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 : n012.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 09:08:55 AM UTC 2026
% Result : Unsatisfiable 159.83s 21.56s
% Output : CNFRefutation 159.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 19 unt; 0 def)
% Number of atoms : 27 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 10 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-5 aty)
% Number of variables : 73 ( 27 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_Int__Oint__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
file('theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).
cnf(c_22,plain,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[clsarity_Int__Oint__OrderedGroup_Ogroup__add]) ).
fof(cls_add__minus__cancel_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),VAR_1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(VAR_0),hAPP(c_HOL_Ouminus__class_Ouminus(VAR_0),VAR_1)),VAR_2)) = VAR_2
| ~ class_OrderedGroup_Ogroup__add(VAR_0) ),
file('theBenchmark.p',cls_add__minus__cancel_0) ).
cnf(c_33,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C)) = C
| ~ class_OrderedGroup_Ogroup__add(A) ),
inference(clausify,[status(thm)],[cls_add__minus__cancel_0]) ).
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_395,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(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
cnf(c_398,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1]) ).
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_915,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_917,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 != hAPP(c_Suc,VAR_0),
file('theBenchmark.p',cls_n__not__Suc__n_0) ).
cnf(c_1073,plain,
A != hAPP(c_Suc,A),
inference(clausify,[status(thm)],[cls_n__not__Suc__n_0]) ).
cnf(c_1074,plain,
hAPP(c_Suc,A) != A,
inference(copy,[status(thm)],[c_1073]) ).
cnf(c_1369,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),B)) = B,
inference(resolve,[status(thm)],[c_33,c_22]) ).
cnf(c_1759,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = A,
inference(resolve,[status(thm)],[c_395,c_398]) ).
cnf(c_3527,plain,
hAPP(c_COMBB(c_Suc,A,B,C,D),E) != hAPP(A,E),
inference(paramod,[status(thm)],[c_915,c_1074]) ).
cnf(c_6940,plain,
hAPP(c_COMBS(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A,B,C,D),E) = hAPP(E,hAPP(A,E)),
inference(paramod,[status(thm)],[c_1759,c_917]) ).
cnf(c_9213,plain,
hAPP(c_COMBB(c_Suc,c_COMBB(A,B,C,D,E),F,V6,V7),V8) != hAPP(A,hAPP(B,V8)),
inference(paramod,[status(thm)],[c_915,c_3527]) ).
cnf(c_20830,plain,
hAPP(c_COMBB(c_Suc,c_COMBB(A,hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C,D,E),F,V6,V7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B)),V8)) != hAPP(A,V8),
inference(paramod,[status(thm)],[c_1369,c_9213]) ).
cnf(c_20832,plain,
hAPP(E,hAPP(A,E)) = hAPP(c_COMBS(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A,B,C,D),E),
inference(copy,[status(thm)],[c_6940]) ).
cnf(c_20831,plain,
$false,
inference(resolve,[status(thm)],[c_20830,c_20832]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV668-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 26 14:44:19 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.31 % Process 848789 was started by sandbox on n012,
% 0.03/0.31 % Sat Sep 26 14:44:19 2026
% 0.03/0.31 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.33
% 0.07/0.33 % From the command line: assign(max_seconds, 300).
% 159.83/21.56
% 159.83/21.56 % given #500 (I,wt=37): 1466 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(122,a,119,a)].
% 159.83/21.56
% 159.83/21.56 % given #1000 (T,wt=19): 13904 c_HOL_Oord__class_Oless(c_Int_OMin,c_Int_OPls,tc_nat) | -c_HOL_Oord__class_Oless(c_Int_OMin,c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(13521,a,1337,b),unit_del(b,940)].
% 159.83/21.56
% 159.83/21.56 % SZS status Unsatisfiable for theBenchmark
% 159.83/21.56
% 159.83/21.56 % Proof 1 at 4.55 (+ 0.55) seconds.
% 159.83/21.56 % Length of proof is 15.
% 159.83/21.56 % Level of proof is 5.
% 159.83/21.56 % Maximum clause weight is 64.000.
% 159.83/21.56 % Given clauses 1220.
% 159.83/21.56
% 159.83/21.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------