%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL856-1 : 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 : n011.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 0.15s 0.55s
% Output : CNFRefutation 0.15s
% 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 : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-3 aty)
% Number of variables : 8 ( 2 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_IT__implies__termi_0,axiom,
! [VAR_0] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,VAR_0))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),VAR_0,tc_Lambda_OdB) ),
file('theBenchmark.p',cls_IT__implies__termi_0) ).
cnf(c_170,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,A))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),A,tc_Lambda_OdB) ),
inference(clausify,[status(thm)],[cls_IT__implies__termi_0]) ).
fof(cls_type__implies__IT_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_Type_Otyping(VAR_1,VAR_0,VAR_2)
| hBOOL(hAPP(c_InductTermi_OIT,VAR_0)) ),
file('theBenchmark.p',cls_type__implies__IT_0) ).
cnf(c_199,plain,
( ~ c_Type_Otyping(B,A,C)
| hBOOL(hAPP(c_InductTermi_OIT,A)) ),
inference(clausify,[status(thm)],[cls_type__implies__IT_0]) ).
fof(cls_conjecture_0,axiom,
c_Type_Otyping(v_e,v_t,v_T),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_201,plain,
c_Type_Otyping(v_e,v_t,v_T),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_202,plain,
~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_876,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_t)),
inference(resolve,[status(thm)],[c_201,c_199]) ).
cnf(c_1080,plain,
c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB),
inference(resolve,[status(thm)],[c_876,c_170]) ).
cnf(c_1079,plain,
$false,
inference(resolve,[status(thm)],[c_202,c_1080]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL856-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n011.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Fri Sep 25 23:43:58 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 3197006 was started by sandbox on n011,
% 0.15/0.43 % Fri Sep 25 23:43:58 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.44
% 0.15/0.44 % From the command line: assign(max_seconds, 300).
% 0.15/0.55
% 0.15/0.55 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.55
% 0.15/0.55 % Proof 1 at 0.08 (+ 0.02) seconds.
% 0.15/0.55 % Length of proof is 6.
% 0.15/0.55 % Level of proof is 2.
% 0.15/0.55 % Maximum clause weight is 21.000.
% 0.15/0.55 % Given clauses 202.
% 0.15/0.55
% 0.15/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------