%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL746-1 : 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 : n016.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 07:59:37 AM UTC 2026
% Result : Unsatisfiable 83.63s 12.01s
% Output : CNFRefutation 83.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 20 unt; 0 def)
% Number of atoms : 40 ( 33 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 27 ( 17 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 78 ( 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_45,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_59,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_Oadd__c_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_Oadd__c_0) ).
cnf(c_64,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_Oadd__c_0]) ).
cnf(c_165,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_45,c_64]) ).
cnf(c_170,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A,
inference(resolve,[status(thm)],[c_45,c_59]) ).
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_183,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_185,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__shift_0,axiom,
! [VAR_0,VAR_1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(VAR_0)),VAR_1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),VAR_0),c_Suc(VAR_1)),
file('theBenchmark.p',cls_add__Suc__shift_0) ).
cnf(c_375,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(A)),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B)),
inference(clausify,[status(thm)],[cls_add__Suc__shift_0]) ).
fof(cls_nat_Osimps_I2_J_0,axiom,
! [VAR_0] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(VAR_0),
file('theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
cnf(c_380,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(A),
inference(clausify,[status(thm)],[cls_nat_Osimps_I2_J_0]) ).
cnf(c_381,plain,
c_Suc(A) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(copy,[status(thm)],[c_380]) ).
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_466,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_8506,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_466]) ).
cnf(c_467,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_8506]) ).
cnf(c_849,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_170,c_185]) ).
cnf(c_8507,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Suc(B)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(A)),B) != A ),
inference(paramod,[status(thm)],[c_375,c_467]) ).
cnf(c_8508,plain,
( c_Suc(B) = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(A)),B) != A ),
inference(copy,[status(thm)],[c_8507]) ).
cnf(c_5159,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(A)),B) != A,
inference(resolve,[status(thm)],[c_381,c_8508]) ).
cnf(c_7911,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B)) != B,
inference(paramod,[status(thm)],[c_165,c_5159]) ).
cnf(c_8277,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(A)),B) != B,
inference(paramod,[status(thm)],[c_375,c_7911]) ).
cnf(c_8504,plain,
hAPP(hAPP(c_COMBB(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(A)),B,C,D),E),F) != hAPP(E,F),
inference(paramod,[status(thm)],[c_183,c_8277]) ).
cnf(c_8509,plain,
hAPP(hAPP(A,E),E) = hAPP(c_COMBS(A,hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B,C,D),E),
inference(copy,[status(thm)],[c_849]) ).
cnf(c_8505,plain,
$false,
inference(resolve,[status(thm)],[c_8504,c_8509]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL746-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n016.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Fri Sep 25 23:33:14 UTC 2026
% 0.10/0.34 % CPUTime :
% 0.10/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.34 % Process 3568389 was started by sandbox2 on n016,
% 0.10/0.34 % Fri Sep 25 23:33:14 2026
% 0.10/0.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 83.63/12.01
% 83.63/12.01 % SZS status Unsatisfiable for theBenchmark
% 83.63/12.01
% 83.63/12.01 % Proof 1 at 2.90 (+ 0.60) seconds.
% 83.63/12.01 % Length of proof is 18.
% 83.63/12.01 % Level of proof is 6.
% 83.63/12.01 % Maximum clause weight is 18.000.
% 83.63/12.01 % Given clauses 404.
% 83.63/12.01
% 83.63/12.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------