%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL826-1 : 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 07:59:51 AM UTC 2026
% Result : Unsatisfiable 3.21s 0.82s
% Output : CNFRefutation 3.21s
% 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 : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 12 ( 3 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Cons_I1_J_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),VAR_2),VAR_1),v_T____)),v_a____),VAR_3))
| ~ hBOOL(hAPP(c_InductTermi_OIT,VAR_0))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,VAR_2),VAR_0),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),VAR_0),VAR_1))) ),
file('theBenchmark.p',cls_Cons_I1_J_0) ).
cnf(c_405,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),C),B),v_T____)),v_a____),D))
| ~ hBOOL(hAPP(c_InductTermi_OIT,A))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,C),A),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),A),B))) ),
inference(clausify,[status(thm)],[cls_Cons_I1_J_0]) ).
fof(cls_conjecture_0,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_a____),v_xa)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_438,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_a____),v_xa)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_xb)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_439,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_xb)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_2,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_440,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_3,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_xb),v_xc))),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_441,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_xb),v_xc))),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
cnf(c_1461,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),A),v_T____)),v_a____),B))
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_xb))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_xb),A))) ),
inference(resolve,[status(thm)],[c_405,c_440]) ).
cnf(c_1462,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),A),v_T____)),v_a____),B))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_xb),A))) ),
inference(resolve,[status(thm)],[c_1461,c_439]) ).
cnf(c_1463,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_xb),v_xc))),
inference(resolve,[status(thm)],[c_1462,c_438]) ).
cnf(c_1460,plain,
$false,
inference(resolve,[status(thm)],[c_441,c_1463]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL826-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.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 23:41:08 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 1423169 was started by sandbox2 on n003,
% 0.10/0.37 % Fri Sep 25 23:41:08 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 3.21/0.82
% 3.21/0.82 % SZS status Unsatisfiable for theBenchmark
% 3.21/0.82
% 3.21/0.82 % Proof 1 at 0.34 (+ 0.08) seconds.
% 3.21/0.82 % Length of proof is 6.
% 3.21/0.82 % Level of proof is 1.
% 3.21/0.82 % Maximum clause weight is 127.000.
% 3.21/0.82 % Given clauses 207.
% 3.21/0.82
% 3.21/0.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------