%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL808-1 : 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 : n019.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 07:59:48 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 10 unt; 0 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 23 ( 14 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-4 aty)
% Number of variables : 12 ( 4 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_36,plain,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_b____,v_u____,v_i____)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_CHAINED_0_03,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('theBenchmark.p',cls_CHAINED_0_03) ).
cnf(c_37,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(clausify,[status(thm)],[cls_CHAINED_0_03]) ).
fof(cls_CHAINED_0_02,axiom,
c_InductTermi_OIT(v_u____),
file('theBenchmark.p',cls_CHAINED_0_02) ).
cnf(c_38,plain,
c_InductTermi_OIT(v_u____),
inference(clausify,[status(thm)],[cls_CHAINED_0_02]) ).
fof(cls_CHAINED_0_01,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_Type_Otyping(c_Type_Oshift(VAR_2,VAR_1,v_T____,tc_Type_Otype),v_b____,VAR_3)
| ~ c_InductTermi_OIT(VAR_0)
| ~ c_Type_Otyping(VAR_2,VAR_0,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,VAR_0,VAR_1)) ),
file('theBenchmark.p',cls_CHAINED_0_01) ).
cnf(c_39,plain,
( ~ c_Type_Otyping(c_Type_Oshift(C,B,v_T____,tc_Type_Otype),v_b____,D)
| ~ c_InductTermi_OIT(A)
| ~ c_Type_Otyping(C,A,v_T____)
| c_InductTermi_OIT(c_Lambda_Osubst(v_b____,A,B)) ),
inference(clausify,[status(thm)],[cls_CHAINED_0_01]) ).
fof(cls_CHAINED_0,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_b____,v_Ua____),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_40,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_b____,v_Ua____),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
cnf(c_90,plain,
( ~ c_Type_Otyping(c_Type_Oshift(A,v_i____,v_T____,tc_Type_Otype),v_b____,B)
| ~ c_InductTermi_OIT(v_u____)
| ~ c_Type_Otyping(A,v_u____,v_T____) ),
inference(resolve,[status(thm)],[c_39,c_36]) ).
cnf(c_91,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_b____,A)
| ~ c_InductTermi_OIT(v_u____) ),
inference(resolve,[status(thm)],[c_90,c_37]) ).
cnf(c_88,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_b____,A),
inference(resolve,[status(thm)],[c_91,c_38]) ).
cnf(c_89,plain,
$false,
inference(resolve,[status(thm)],[c_88,c_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL808-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 23:36:48 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 3998105 was started by sandbox2 on n019,
% 0.11/0.37 % Fri Sep 25 23:36:48 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.39
% 0.11/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.39
% 0.11/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.11/0.39 % Length of proof is 7.
% 0.11/0.39 % Level of proof is 2.
% 0.11/0.39 % Maximum clause weight is 19.000.
% 0.11/0.39 % Given clauses 12.
% 0.11/0.39
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------