%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL838-1 : 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 : n006.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 07:59:54 AM UTC 2026
% Result : Unsatisfiable 0.91s 0.51s
% Output : CNFRefutation 0.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% 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 : 11 ( 7 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 2 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 11 con; 0-5 aty)
% Number of variables : 11 ( 2 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
~ v_thesis____,
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_117,plain,
~ v_thesis____,
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_CHAINED_0,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_118,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
fof(cls_that_0,axiom,
! [VAR_0] :
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),VAR_0)
| v_thesis____ ),
file('theBenchmark.p',cls_that_0) ).
cnf(c_136,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),A)
| v_thesis____ ),
inference(clausify,[status(thm)],[cls_that_0]) ).
cnf(c_137,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),A),
inference(resolve,[status(thm)],[c_117,c_136]) ).
fof(cls_list__app__typeE_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_Type_Otyping(VAR_0,c_List_Ofoldl(c_Lambda_OdB_OApp,VAR_1,VAR_3,tc_Lambda_OdB,tc_Lambda_OdB),VAR_2)
| c_Type_Otyping(VAR_0,VAR_1,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(VAR_2,VAR_0,VAR_1,VAR_3),VAR_2,tc_Type_Otype,tc_Type_Otype)) ),
file('theBenchmark.p',cls_list__app__typeE_0) ).
cnf(c_255,plain,
( ~ c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,B,D,tc_Lambda_OdB,tc_Lambda_OdB),C)
| c_Type_Otyping(A,B,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(C,A,B,D),C,tc_Type_Otype,tc_Type_Otype)) ),
inference(clausify,[status(thm)],[cls_list__app__typeE_0]) ).
cnf(c_958,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____),v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(resolve,[status(thm)],[c_255,c_118]) ).
cnf(c_957,plain,
$false,
inference(resolve,[status(thm)],[c_137,c_958]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL838-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.36 % Computer : n006.cluster.edu
% 0.02/0.36 % Model : x86_64 x86_64
% 0.02/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.36 % Memory : 8046.5625MB
% 0.02/0.36 % OS : Linux 6.8.0-71-generic
% 0.02/0.36 % CPULimit : 300
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Fri Sep 25 23:42:10 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.36 % Process 4037106 was started by sandbox on n006,
% 0.02/0.36 % Fri Sep 25 23:42:10 2026
% 0.02/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.02/0.38
% 0.02/0.38 % From the command line: assign(max_seconds, 300).
% 0.91/0.51
% 0.91/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.91/0.51
% 0.91/0.51 % Proof 1 at 0.10 (+ 0.02) seconds.
% 0.91/0.51 % Length of proof is 6.
% 0.91/0.51 % Level of proof is 2.
% 0.91/0.51 % Maximum clause weight is 45.000.
% 0.91/0.51 % Given clauses 146.
% 0.91/0.51
% 0.91/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------