%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL818-1 : 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 : n020.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 07:59:50 AM UTC 2026
% Result : Unsatisfiable 4.50s 1.07s
% Output : CNFRefutation 4.50s
% 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 : 9 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-5 aty)
% Number of variables : 12 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
~ c_Type_Otyping(v_e____,hAPP(hAPP(c_Lambda_OdB_OApp,v_u____),c_Lambda_Osubst(v_a____,v_u____,v_i____)),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_118,plain,
~ c_Type_Otyping(v_e____,hAPP(hAPP(c_Lambda_OdB_OApp,v_u____),c_Lambda_Osubst(v_a____,v_u____,v_i____)),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]) ).
fof(cls_CHAINED_0_01,axiom,
c_Type_Otyping(v_e____,v_u____,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_CHAINED_0_01) ).
cnf(c_119,plain,
c_Type_Otyping(v_e____,v_u____,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_CHAINED_0_01]) ).
fof(cls_CHAINED_0,axiom,
c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_120,plain,
c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
fof(cls_App_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ c_Type_Otyping(VAR_0,VAR_1,hAPP(hAPP(c_Type_Otype_OFun,VAR_4),VAR_3))
| ~ c_Type_Otyping(VAR_0,VAR_2,VAR_4)
| c_Type_Otyping(VAR_0,hAPP(hAPP(c_Lambda_OdB_OApp,VAR_1),VAR_2),VAR_3) ),
file('theBenchmark.p',cls_App_0) ).
cnf(c_165,plain,
( ~ c_Type_Otyping(A,B,hAPP(hAPP(c_Type_Otype_OFun,E),D))
| ~ c_Type_Otyping(A,C,E)
| c_Type_Otyping(A,hAPP(hAPP(c_Lambda_OdB_OApp,B),C),D) ),
inference(clausify,[status(thm)],[cls_App_0]) ).
cnf(c_521,plain,
( ~ c_Type_Otyping(v_e____,A,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),B))
| c_Type_Otyping(v_e____,hAPP(hAPP(c_Lambda_OdB_OApp,A),c_Lambda_Osubst(v_a____,v_u____,v_i____)),B) ),
inference(resolve,[status(thm)],[c_165,c_120]) ).
cnf(c_2495,plain,
c_Type_Otyping(v_e____,hAPP(hAPP(c_Lambda_OdB_OApp,v_u____),c_Lambda_Osubst(v_a____,v_u____,v_i____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(resolve,[status(thm)],[c_521,c_119]) ).
cnf(c_2494,plain,
$false,
inference(resolve,[status(thm)],[c_118,c_2495]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL818-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n020.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Fri Sep 25 23:39:03 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 4087023 was started by sandbox on n020,
% 0.12/0.38 % Fri Sep 25 23:39:03 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.40
% 0.12/0.40 % From the command line: assign(max_seconds, 300).
% 4.50/1.07
% 4.50/1.07 % given #500 (F,wt=21): 966 hAPP(hAPP(c_Lambda_OdB_OApp,A),B) != c_Lambda_Olift(c_Lambda_Osubst(c_Lambda_OdB_OAbs(C),D,E),F). [para(403(a,1),815(a,2,1))].
% 4.50/1.07
% 4.50/1.07 % SZS status Unsatisfiable for theBenchmark
% 4.50/1.07
% 4.50/1.07 % Proof 1 at 0.51 (+ 0.11) seconds.
% 4.50/1.07 % Length of proof is 6.
% 4.50/1.07 % Level of proof is 2.
% 4.50/1.07 % Maximum clause weight is 26.000.
% 4.50/1.07 % Given clauses 666.
% 4.50/1.07
% 4.50/1.07 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------