%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG376-1 : 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 06:50:06 AM UTC 2026
% Result : Unsatisfiable 27.16s 9.32s
% Output : CNFRefutation 27.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 7 unt; 0 def)
% Number of atoms : 15 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 10 con; 0-3 aty)
% Number of variables : 6 ( 1 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_le__add1_0,axiom,
! [VAR_0,VAR_1] : c_lessequals(VAR_0,c_HOL_Oplus__class_Oplus(VAR_0,VAR_1,tc_nat),tc_nat),
file('theBenchmark.p',cls_le__add1_0) ).
cnf(c_1598,plain,
c_lessequals(A,c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),
inference(clausify,[status(thm)],[cls_le__add1_0]) ).
fof(cls_th1_0,axiom,
! [VAR_0] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(VAR_0,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_d____,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,VAR_0,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('theBenchmark.p',cls_th1_0) ).
cnf(c_1691,plain,
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(A,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_d____,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,A,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[cls_th1_0]) ).
fof(cls_CHAINED_0_01,axiom,
( ~ c_lessequals(v_N1____,c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_g____(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_d____,tc_RealDef_Oreal) ),
file('theBenchmark.p',cls_CHAINED_0_01) ).
cnf(c_1784,plain,
( ~ c_lessequals(v_N1____,c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_g____(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_d____,tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[cls_CHAINED_0_01]) ).
cnf(c_1785,plain,
c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_g____(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_d____,tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_1598,c_1784]) ).
fof(cls_conjecture_0,axiom,
~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_g____(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1786,plain,
~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_g____(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_8072,plain,
c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_g____(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_1785,c_1691]) ).
cnf(c_8071,plain,
$false,
inference(resolve,[status(thm)],[c_1786,c_8072]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG376-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n013.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sat Sep 26 21:55:33 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 3629474 was started by sandbox on n013,
% 0.10/5.38 % Sat Sep 26 21:55:33 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/5.42
% 0.14/5.42 % From the command line: assign(max_seconds, 300).
% 27.16/9.32
% 27.16/9.32 % given #500 (I,wt=43): 1488 -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),A),D,A) = c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(C,A),D,A),A). [copy(1487),flip(b)].
% 27.16/9.32
% 27.16/9.32 % SZS status Unsatisfiable for theBenchmark
% 27.16/9.32
% 27.16/9.32 % Proof 1 at 3.57 (+ 0.27) seconds.
% 27.16/9.32 % Length of proof is 6.
% 27.16/9.32 % Level of proof is 2.
% 27.16/9.32 % Maximum clause weight is 74.000.
% 27.16/9.32 % Given clauses 738.
% 27.16/9.32
% 27.16/9.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------