%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG377-1 : 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 : n010.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 0.13s 10.70s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 12 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_add__left__mono_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_lessequals(VAR_2,VAR_3,VAR_0)
| c_lessequals(c_HOL_Oplus__class_Oplus(VAR_1,VAR_2,VAR_0),c_HOL_Oplus__class_Oplus(VAR_1,VAR_3,VAR_0),VAR_0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(VAR_0) ),
file('theBenchmark.p',cls_add__left__mono_0) ).
cnf(c_363,plain,
( ~ c_lessequals(C,D,A)
| c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(A) ),
inference(clausify,[status(thm)],[cls_add__left__mono_0]) ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add) ).
cnf(c_366,plain,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add]) ).
cnf(c_381,plain,
( ~ c_lessequals(B,C,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolve,[status(thm)],[c_366,c_363]) ).
fof(cls_conjecture_0,axiom,
~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_537,plain,
~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_CHAINED_0,axiom,
c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_538,plain,
c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
cnf(c_1291,plain,
c_lessequals(c_HOL_Oplus__class_Oplus(A,c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(A,c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_538,c_381]) ).
cnf(c_1292,plain,
$false,
inference(resolve,[status(thm)],[c_1291,c_537]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG377-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/10.39 % Computer : n010.cluster.edu
% 0.10/10.39 % Model : x86_64 x86_64
% 0.10/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39 % Memory : 8046.5625MB
% 0.10/10.39 % OS : Linux 6.8.0-71-generic
% 0.10/10.39 % CPULimit : 300
% 0.10/10.39 % WCLimit : 300
% 0.10/10.39 % DateTime : Sat Sep 26 21:56:26 UTC 2026
% 0.10/10.39 % CPUTime :
% 0.10/10.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/10.39 % Process 100746 was started by sandbox2 on n010,
% 0.10/10.39 % Sat Sep 26 21:56:26 2026
% 0.10/10.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/10.41
% 0.13/10.41 % From the command line: assign(max_seconds, 300).
% 0.13/10.70
% 0.13/10.70 % SZS status Unsatisfiable for theBenchmark
% 0.13/10.70
% 0.13/10.70 % Proof 1 at 0.26 (+ 0.01) seconds.
% 0.13/10.70 % Length of proof is 7.
% 0.13/10.70 % Level of proof is 3.
% 0.13/10.70 % Maximum clause weight is 70.000.
% 0.13/10.70 % Given clauses 130.
% 0.13/10.70
% 0.13/10.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------