%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL855-1 : 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 : n026.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 07:59:56 AM UTC 2026
% Result : Unsatisfiable 0.76s 0.52s
% Output : CNFRefutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 16 unt; 0 def)
% Number of atoms : 16 ( 9 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 : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 30 ( 1 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,v_ta____)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_151,plain,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,v_ta____)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_CHAINED_0,axiom,
c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_152,plain,
c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))),
inference(clausify,[status(thm)],[cls_CHAINED_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_173,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_174,plain,
c_Lambda_OdB_OApp(c_Lambda_Osubst(A,B,C),c_Lambda_Osubst(D,B,C)) = c_Lambda_Osubst(c_Lambda_OdB_OApp(A,D),B,C),
inference(copy,[status(thm)],[c_173]) ).
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_177,plain,
c_Lambda_Osubst(c_Lambda_OdB_OVar(A),B,A) = B,
inference(clausify,[status(thm)],[cls_subst__eq_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_194,plain,
c_Lambda_Osubst(c_Lambda_Olift(A,B),C,B) = A,
inference(clausify,[status(thm)],[cls_subst__lift_0]) ).
cnf(c_513,plain,
c_Lambda_OdB_OApp(c_Lambda_Osubst(A,B,C),D) = c_Lambda_Osubst(c_Lambda_OdB_OApp(A,c_Lambda_Olift(D,C)),B,C),
inference(paramod,[status(thm)],[c_194,c_174]) ).
cnf(c_505,plain,
c_Lambda_Osubst(c_Lambda_OdB_OApp(A,c_Lambda_Olift(B,C)),D,C) = c_Lambda_OdB_OApp(c_Lambda_Osubst(A,D,C),B),
inference(copy,[status(thm)],[c_513]) ).
cnf(c_514,plain,
c_InductTermi_OIT(c_Lambda_OdB_OApp(c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)),v_ta____)),
inference(paramod,[status(thm)],[c_505,c_152]) ).
cnf(c_515,plain,
c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,v_ta____)),
inference(paramod,[status(thm)],[c_177,c_514]) ).
cnf(c_512,plain,
$false,
inference(resolve,[status(thm)],[c_151,c_515]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL855-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 23:46:39 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3754675 was started by sandbox on n026,
% 0.10/0.37 % Fri Sep 25 23:46:39 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.76/0.52
% 0.76/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.76/0.52
% 0.76/0.52 % Proof 1 at 0.11 (+ 0.02) seconds.
% 0.76/0.52 % Length of proof is 8.
% 0.76/0.52 % Level of proof is 3.
% 0.76/0.52 % Maximum clause weight is 38.000.
% 0.76/0.52 % Given clauses 61.
% 0.76/0.52
% 0.76/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------