%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL755-1 : 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 : n009.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 07:59:39 AM UTC 2026
% Result : Unsatisfiable 3.53s 0.97s
% Output : CNFRefutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 10 unt; 0 def)
% Number of atoms : 14 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 6 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 10 ( 4 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_2,axiom,
~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_410,plain,
~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0,VAR_1] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(VAR_0),VAR_1)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_411,plain,
c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(A),B)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_Lambda_0,axiom,
! [VAR_0] :
( ~ c_InductTermi_OIT(VAR_0)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(VAR_0)) ),
file('theBenchmark.p',cls_Lambda_0) ).
cnf(c_425,plain,
( ~ c_InductTermi_OIT(A)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(A)) ),
inference(clausify,[status(thm)],[cls_Lambda_0]) ).
fof(cls_Suc__eq__plus1_0,axiom,
! [VAR_0] : c_Suc(VAR_0) = c_HOL_Oplus__class_Oplus(VAR_0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('theBenchmark.p',cls_Suc__eq__plus1_0) ).
cnf(c_704,plain,
c_Suc(A) = c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(clausify,[status(thm)],[cls_Suc__eq__plus1_0]) ).
cnf(c_1535,plain,
~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(v_ia,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_Suc(v_ja)))),
inference(paramod,[status(thm)],[c_704,c_410]) ).
cnf(c_877,plain,
~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(v_ia,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_HOL_Oplus__class_Oplus(v_ja,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))),
inference(paramod,[status(thm)],[c_704,c_1535]) ).
cnf(c_1533,plain,
c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(A),B))),
inference(resolve,[status(thm)],[c_425,c_411]) ).
cnf(c_1534,plain,
$false,
inference(resolve,[status(thm)],[c_1533,c_877]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL755-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.38 % Computer : n009.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Fri Sep 25 23:29:59 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.39 % Process 2825541 was started by sandbox2 on n009,
% 0.13/0.39 % Fri Sep 25 23:29:59 2026
% 0.13/0.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.41
% 0.13/0.41 % From the command line: assign(max_seconds, 300).
% 3.53/0.97
% 3.53/0.97 % SZS status Unsatisfiable for theBenchmark
% 3.53/0.97
% 3.53/0.97 % Proof 1 at 0.49 (+ 0.05) seconds.
% 3.53/0.97 % Length of proof is 7.
% 3.53/0.97 % Level of proof is 2.
% 3.53/0.97 % Maximum clause weight is 45.000.
% 3.53/0.97 % Given clauses 105.
% 3.53/0.97
% 3.53/0.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------