%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL838-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 : Mon Sep 7 01:08:34 PM UTC 2026
% Result : Unsatisfiable 108.45s 108.72s
% Output : Refutation 108.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 10 ( 8 unt; 0 nHn; 10 RR)
% Number of literals : 12 ( 0 equ; 6 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 2 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 17 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(43,axiom,
equal(c_List_Ofoldl(u,v,c_List_Olist_OCons(w,x,y),z,y),c_List_Ofoldl(u,hAPP(hAPP(u,v),w),x,z,y)),
file('LCL838-1.p',unknown),
[] ).
cnf(277,axiom,
( ~ c_Type_Otyping(u,c_List_Ofoldl(c_Lambda_OdB_OApp,v,w,tc_Lambda_OdB,tc_Lambda_OdB),x)
| c_Type_Otyping(u,v,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(x,u,v,w),x,tc_Type_Otype,tc_Type_Otype)) ),
file('LCL838-1.p',unknown),
[] ).
cnf(417,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('LCL838-1.p',unknown),
[] ).
cnf(441,axiom,
~ v_thesis____,
file('LCL838-1.p',unknown),
[] ).
cnf(442,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_OAbs(v_r____)),v_a____),u)
| v_thesis____ ),
file('LCL838-1.p',unknown),
[] ).
cnf(447,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____),u),
inference(mrr,[status(thm)],[442,441]),
[iquote('0:MRR:442.1,441.0')] ).
cnf(472,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____),c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(rew,[status(thm),theory(equality)],[43,417]),
[iquote('0:Rew:43.0,417.0')] ).
cnf(54636,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____),u,tc_Lambda_OdB,tc_Lambda_OdB),v),
inference(res,[status(thm),theory(equality)],[277,447]),
[iquote('0:Res:277.1,447.0')] ).
cnf(54646,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____),c_List_Olist_OCons(v_a____,u,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v),
inference(rew,[status(thm),theory(equality)],[43,54636]),
[iquote('0:Rew:43.0,54636.0')] ).
cnf(54647,plain,
$false,
inference(unc,[status(thm)],[54646,472]),
[iquote('0:UnC:54646.0,472.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL838-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 5 02:16:36 UTC 2026
% 0.10/0.37 % CPUTime :
% 108.45/108.72
% 108.45/108.72 SPASS V 3.9
% 108.45/108.72 SPASS beiseite: Proof found.
% 108.45/108.72 % SZS status Theorem
% 108.45/108.72 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 108.45/108.72 SPASS derived 45085 clauses, backtracked 0 clauses, performed 0 splits and kept 11479 clauses.
% 108.45/108.72 SPASS allocated 113330 KBytes.
% 108.45/108.72 SPASS spent 0:1:46.47 on the problem.
% 108.45/108.72 0:00:00.07 for the input.
% 108.45/108.72 0:00:00.00 for the FLOTTER CNF translation.
% 108.45/108.72 0:00:01.43 for inferences.
% 108.45/108.72 0:00:00.00 for the backtracking.
% 108.45/108.72 0:1:44.26 for the reduction.
% 108.45/108.72
% 108.45/108.72
% 108.45/108.72 Here is a proof with depth 1, length 10 :
% 108.45/108.72 % SZS output start Refutation
% See solution above
% 108.45/108.72 Formulae used in the proof : cls_foldl__Cons_0 cls_list__app__typeE_0 cls_CHAINED_0 cls_conjecture_0 cls_conjecture_1
% 108.45/108.72
%------------------------------------------------------------------------------