%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL800-1 : 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 : n003.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 07:59:46 AM UTC 2026
% Result : Unsatisfiable 0.13s 5.54s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 6 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 18 ( 1 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_i____))),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_152,plain,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_i____))),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_CHAINED_0,axiom,
c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_153,plain,
c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
fof(cls_subst__lift_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_Lambda_Osubst(c_Lambda_Olift(VAR_0,VAR_1),VAR_2,VAR_1) = VAR_0,
file('theBenchmark.p',cls_subst__lift_0) ).
cnf(c_159,plain,
c_Lambda_Osubst(c_Lambda_Olift(A,B),C,B) = A,
inference(clausify,[status(thm)],[cls_subst__lift_0]) ).
fof(cls_subst__eq_0,axiom,
! [VAR_0,VAR_1] : c_Lambda_Osubst(c_Lambda_OdB_OVar(VAR_0),VAR_1,VAR_0) = VAR_1,
file('theBenchmark.p',cls_subst__eq_0) ).
cnf(c_175,plain,
c_Lambda_Osubst(c_Lambda_OdB_OVar(A),B,A) = B,
inference(clausify,[status(thm)],[cls_subst__eq_0]) ).
fof(cls_subst__App_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : c_Lambda_Osubst(c_Lambda_OdB_OApp(VAR_0,VAR_1),VAR_2,VAR_3) = c_Lambda_OdB_OApp(c_Lambda_Osubst(VAR_0,VAR_2,VAR_3),c_Lambda_Osubst(VAR_1,VAR_2,VAR_3)),
file('theBenchmark.p',cls_subst__App_0) ).
cnf(c_178,plain,
c_Lambda_Osubst(c_Lambda_OdB_OApp(A,B),C,D) = c_Lambda_OdB_OApp(c_Lambda_Osubst(A,C,D),c_Lambda_Osubst(B,C,D)),
inference(clausify,[status(thm)],[cls_subst__App_0]) ).
cnf(c_371,plain,
c_InductTermi_OIT(c_Lambda_OdB_OApp(c_Lambda_Osubst(c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(paramod,[status(thm)],[c_178,c_153]) ).
cnf(c_372,plain,
c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Osubst(v_a____,v_u____,v_i____),c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(paramod,[status(thm)],[c_159,c_371]) ).
cnf(c_373,plain,
c_InductTermi_OIT(c_Lambda_OdB_OApp(v_u____,c_Lambda_Osubst(v_a____,v_u____,v_i____))),
inference(paramod,[status(thm)],[c_175,c_372]) ).
cnf(c_370,plain,
$false,
inference(resolve,[status(thm)],[c_152,c_373]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL800-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n003.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Fri Sep 25 23:37:14 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.37 % Process 1410861 was started by sandbox2 on n003,
% 0.09/5.37 % Fri Sep 25 23:37:14 2026
% 0.09/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.39
% 0.09/5.39 % From the command line: assign(max_seconds, 300).
% 0.13/5.54
% 0.13/5.54 % SZS status Unsatisfiable for theBenchmark
% 0.13/5.54
% 0.13/5.54 % Proof 1 at 0.14 (+ 0.00) seconds.
% 0.13/5.54 % Length of proof is 6.
% 0.13/5.54 % Level of proof is 1.
% 0.13/5.54 % Maximum clause weight is 16.000.
% 0.13/5.54 % Given clauses 0.
% 0.13/5.54
% 0.13/5.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------