%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL787-1 : 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 : n005.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 143.37s 29.55s
% Output : CNFRefutation 143.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 11 unt; 0 def)
% Number of atoms : 30 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 15 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-5 aty)
% Number of variables : 20 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_typing__elims_I2_J_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_Type_Otyping(VAR_0,hAPP(hAPP(c_Lambda_OdB_OApp,VAR_3),VAR_1),VAR_2)
| c_Type_Otyping(VAR_0,VAR_1,c_Type_Osko__Type__Xtyping__elims__2__1(VAR_2,VAR_0,VAR_3,VAR_1)) ),
file('theBenchmark.p',cls_typing__elims_I2_J_1) ).
cnf(c_287,plain,
( ~ c_Type_Otyping(A,hAPP(hAPP(c_Lambda_OdB_OApp,D),B),C)
| c_Type_Otyping(A,B,c_Type_Osko__Type__Xtyping__elims__2__1(C,A,D,B)) ),
inference(clausify,[status(thm)],[cls_typing__elims_I2_J_1]) ).
fof(cls_True_0,axiom,
v_n____ = v_i____,
file('theBenchmark.p',cls_True_0) ).
cnf(c_396,plain,
v_n____ = v_i____,
inference(clausify,[status(thm)],[cls_True_0]) ).
fof(cls_headT_0,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
file('theBenchmark.p',cls_headT_0) ).
cnf(c_402,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_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(clausify,[status(thm)],[cls_headT_0]) ).
cnf(c_403,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_OVar(v_i____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(paramod,[status(thm)],[c_396,c_402]) ).
fof(cls_that_0,axiom,
! [VAR_0] :
( ~ 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,VAR_0),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,VAR_0)
| v_thesis____ ),
file('theBenchmark.p',cls_that_0) ).
cnf(c_415,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,A),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,A)
| v_thesis____ ),
inference(clausify,[status(thm)],[cls_that_0]) ).
cnf(c_416,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,A),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,A)
| v_thesis____ ),
inference(paramod,[status(thm)],[c_396,c_415]) ).
fof(cls_typing__elims_I2_J_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_Type_Otyping(VAR_0,hAPP(hAPP(c_Lambda_OdB_OApp,VAR_1),VAR_3),VAR_2)
| c_Type_Otyping(VAR_0,VAR_1,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(VAR_2,VAR_0,VAR_1,VAR_3)),VAR_2)) ),
file('theBenchmark.p',cls_typing__elims_I2_J_0) ).
cnf(c_422,plain,
( ~ c_Type_Otyping(A,hAPP(hAPP(c_Lambda_OdB_OApp,B),D),C)
| c_Type_Otyping(A,B,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(C,A,B,D)),C)) ),
inference(clausify,[status(thm)],[cls_typing__elims_I2_J_0]) ).
fof(cls_conjecture_0,axiom,
~ v_thesis____,
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_425,plain,
~ v_thesis____,
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_462,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,A),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,A) ),
inference(resolve,[status(thm)],[c_425,c_416]) ).
cnf(c_1071,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,c_Type_Osko__Type__Xtyping__elims__2__1(c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),v_a____)),
inference(resolve,[status(thm)],[c_403,c_287]) ).
cnf(c_1147,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,c_Type_Osko__Type__Xtyping__elims__2__1(c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
inference(resolve,[status(thm)],[c_422,c_403]) ).
cnf(c_34641,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,c_Type_Osko__Type__Xtyping__elims__2__1(c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
inference(resolve,[status(thm)],[c_1071,c_462]) ).
cnf(c_34640,plain,
$false,
inference(resolve,[status(thm)],[c_1147,c_34641]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL787-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/10.36 % Computer : n005.cluster.edu
% 0.08/10.36 % Model : x86_64 x86_64
% 0.08/10.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.36 % Memory : 8046.5625MB
% 0.08/10.36 % OS : Linux 6.8.0-71-generic
% 0.08/10.36 % CPULimit : 300
% 0.08/10.36 % WCLimit : 300
% 0.08/10.36 % DateTime : Fri Sep 25 23:34:14 UTC 2026
% 0.08/10.37 % CPUTime :
% 0.08/10.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/10.37 % Process 534621 was started by sandbox2 on n005,
% 0.08/10.37 % Fri Sep 25 23:34:14 2026
% 0.08/10.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/10.38
% 0.08/10.38 % From the command line: assign(max_seconds, 300).
% 143.37/29.55
% 143.37/29.55 % given #500 (F,wt=24): 1281 c_List_Oappend(c_List_Olist_OCons(A,c_List_Oreplicate(B,C,D),D),c_List_Oreplicate(E,C,D),D) != c_List_Oappend(c_List_Oreplicate(E,C,D),c_List_Oreplicate(B,C,D),D). [para(136(a,1),827(a,2))].
% 143.37/29.55
% 143.37/29.55 % given #1000 (T,wt=12): 2248 c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_Lambda_Olift(c_Lambda_OdB_OAbs(c_Lambda_Olift(v_u____,A)),B),tc_Lambda_OdB). [resolve(1470,a,117,b)].
% 143.37/29.55
% 143.37/29.55 % given #1500 (F,wt=28): 17587 -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),A,B,tc_nat,tc_nat)),C),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),A,c_List_Oappend(c_List_Olist_OCons(C,c_List_Olist_ONil(tc_nat),tc_nat),B,tc_nat),tc_nat,tc_nat),tc_nat). [para(89(a,1),17582(a,1))].
% 143.37/29.55
% 143.37/29.55 % given #2000 (T,wt=13): 12355 hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(c_Lambda_Olift(c_Lambda_Osubst(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(v_u____)),c_Lambda_OdB_OVar(A),B),C)))). [resolve(3055,a,207,b)].
% 143.37/29.55
% 143.37/29.55 % given #2500 (F,wt=30): 11465 -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),c_List_Oappend(c_List_Olist_OCons(B,c_List_Olist_OCons(C,D,tc_nat),tc_nat),E,tc_nat),tc_nat,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),tc_nat). [para(437(a,1),11311(a,1))].
% 143.37/29.55
% 143.37/29.55 % given #3000 (T,wt=14): 13820 hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(c_Lambda_Olift(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(v_u____)))))),A),B))). [resolve(5270,a,309,b)].
% 143.37/29.55
% 143.37/29.55 % given #3500 (F,wt=30): 27260 -c_HOL_Oord__class_Oless(c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),A,c_List_Oappend(B,c_List_Oappend(c_List_Olist_OCons(C,c_List_Olist_ONil(tc_nat),tc_nat),c_List_Olist_OCons(c_HOL_Ozero__class_Ozero(tc_nat),D,tc_nat),tc_nat),tc_nat),tc_nat,tc_nat),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),C,D,tc_nat,tc_nat),tc_nat). [para(857(a,1),22179(a,2)),rewrite([26368(8)])].
% 143.37/29.55
% 143.37/29.55 % given #4000 (A,wt=26): 1015 c_List_Oappend(A,c_List_Oappend(B,c_List_Olist_OCons(C,c_List_Olist_ONil(D),D),D),D) != c_List_Oappend(E,c_List_Olist_OCons(F,c_List_Olist_ONil(D),D),D) | c_List_Oappend(A,B,D) = E. [para(359(a,1),356(a,1))].
% 143.37/29.55
% 143.37/29.55 % SZS status Unsatisfiable for theBenchmark
% 143.37/29.55
% 143.37/29.55 % Proof 1 at 15.49 (+ 3.46) seconds.
% 143.37/29.55 % Length of proof is 12.
% 143.37/29.55 % Level of proof is 3.
% 143.37/29.55 % Maximum clause weight is 32.000.
% 143.37/29.55 % Given clauses 4405.
% 143.37/29.55
% 143.37/29.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------