%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL788-1 : 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 07:59:44 AM UTC 2026
% Result : Unsatisfiable 0.14s 5.65s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 14 unt; 0 def)
% Number of atoms : 18 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-5 aty)
% Number of variables : 14 ( 2 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
v_T____ != hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_3,plain,
v_T____ != hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_4,plain,
hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) != v_T____,
inference(copy,[status(thm)],[c_3]) ).
fof(cls_CHAINED_0,axiom,
v_n____ = v_i____,
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_6,plain,
v_n____ = v_i____,
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
fof(cls_varT_0,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
file('theBenchmark.p',cls_varT_0) ).
cnf(c_15,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
inference(clausify,[status(thm)],[cls_varT_0]) ).
cnf(c_16,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
inference(paramod,[status(thm)],[c_6,c_15]) ).
fof(cls_shift__eq_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : hAPP(c_Type_Oshift(VAR_0,VAR_1,VAR_2,VAR_3),VAR_1) = VAR_2,
file('theBenchmark.p',cls_shift__eq_0) ).
cnf(c_57,plain,
hAPP(c_Type_Oshift(A,B,C,D),B) = C,
inference(clausify,[status(thm)],[cls_shift__eq_0]) ).
fof(cls_typing__elims_I1_J_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_Type_Otyping(VAR_0,c_Lambda_OdB_OVar(VAR_1),VAR_2)
| hAPP(VAR_0,VAR_1) = VAR_2 ),
file('theBenchmark.p',cls_typing__elims_I1_J_0) ).
cnf(c_59,plain,
( ~ c_Type_Otyping(A,c_Lambda_OdB_OVar(B),C)
| hAPP(A,B) = C ),
inference(clausify,[status(thm)],[cls_typing__elims_I1_J_0]) ).
cnf(c_350,plain,
hAPP(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_i____) = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(resolve,[status(thm)],[c_59,c_16]) ).
cnf(c_351,plain,
v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(paramod,[status(thm)],[c_57,c_350]) ).
cnf(c_352,plain,
hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) = v_T____,
inference(copy,[status(thm)],[c_351]) ).
cnf(c_349,plain,
$false,
inference(resolve,[status(thm)],[c_4,c_352]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL788-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.58 % Computer : n019.cluster.edu
% 0.11/5.58 % Model : x86_64 x86_64
% 0.11/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.58 % Memory : 8046.5625MB
% 0.11/5.58 % OS : Linux 6.8.0-71-generic
% 0.11/5.58 % CPULimit : 300
% 0.11/5.58 % WCLimit : 300
% 0.11/5.58 % DateTime : Fri Sep 25 23:34:11 UTC 2026
% 0.11/5.58 % CPUTime :
% 0.11/5.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.58 % Process 3995528 was started by sandbox2 on n019,
% 0.11/5.58 % Fri Sep 25 23:34:11 2026
% 0.11/5.58 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/5.59
% 0.11/5.59 % From the command line: assign(max_seconds, 300).
% 0.14/5.65
% 0.14/5.65 % SZS status Unsatisfiable for theBenchmark
% 0.14/5.65
% 0.14/5.65 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.14/5.65 % Length of proof is 8.
% 0.14/5.65 % Level of proof is 2.
% 0.14/5.65 % Maximum clause weight is 35.000.
% 0.14/5.65 % Given clauses 29.
% 0.14/5.65
% 0.14/5.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------