%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL814-1 : 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 : n004.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 07:59:49 AM UTC 2026
% Result : Unsatisfiable 5.36s 1.17s
% Output : CNFRefutation 5.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-4 aty)
% Number of variables : 13 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_uT_0,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('theBenchmark.p',cls_uT_0) ).
cnf(c_782,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(clausify,[status(thm)],[cls_uT_0]) ).
fof(cls_argsT_0,axiom,
c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____),
file('theBenchmark.p',cls_argsT_0) ).
cnf(c_806,plain,
c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____),
inference(clausify,[status(thm)],[cls_argsT_0]) ).
fof(cls_substs__lemma_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ c_Type_Otyping(VAR_0,VAR_1,VAR_5)
| ~ c_Type_Otypings(c_Type_Oshift(VAR_0,VAR_2,VAR_5,tc_Type_Otype),VAR_3,VAR_4)
| c_Type_Otypings(VAR_0,c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),VAR_1),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),VAR_2),VAR_3,tc_Lambda_OdB,tc_Lambda_OdB),VAR_4) ),
file('theBenchmark.p',cls_substs__lemma_0) ).
cnf(c_818,plain,
( ~ c_Type_Otyping(A,B,F)
| ~ c_Type_Otypings(c_Type_Oshift(A,C,F,tc_Type_Otype),D,E)
| c_Type_Otypings(A,c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),B),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),C),D,tc_Lambda_OdB,tc_Lambda_OdB),E) ),
inference(clausify,[status(thm)],[cls_substs__lemma_0]) ).
fof(cls_conjecture_0,axiom,
~ c_Type_Otypings(v_e____,c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_830,plain,
~ c_Type_Otypings(v_e____,c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_3980,plain,
( ~ c_Type_Otyping(v_e____,A,v_T____)
| c_Type_Otypings(v_e____,c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),A),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____) ),
inference(resolve,[status(thm)],[c_818,c_806]) ).
cnf(c_3981,plain,
c_Type_Otypings(v_e____,c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
inference(resolve,[status(thm)],[c_3980,c_782]) ).
cnf(c_3979,plain,
$false,
inference(resolve,[status(thm)],[c_830,c_3981]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL814-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n004.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 23:37:22 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 254895 was started by sandbox on n004,
% 0.11/0.37 % Fri Sep 25 23:37:22 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 5.36/1.17
% 5.36/1.17 % SZS status Unsatisfiable for theBenchmark
% 5.36/1.17
% 5.36/1.17 % Proof 1 at 0.67 (+ 0.09) seconds.
% 5.36/1.17 % Length of proof is 5.
% 5.36/1.17 % Level of proof is 1.
% 5.36/1.17 % Maximum clause weight is 69.000.
% 5.36/1.17 % Given clauses 431.
% 5.36/1.17
% 5.36/1.17 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------