%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL785-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 01:08:24 PM UTC 2026
% Result : Unsatisfiable 0.31s 0.58s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 10 ( 10 unt; 0 nHn; 10 RR)
% Number of literals : 10 ( 0 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 17 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(350,axiom,
equal(v_i____,v_n____),
file('LCL785-1.p',unknown),
[] ).
cnf(369,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('LCL785-1.p',unknown),
[] ).
cnf(394,axiom,
equal(c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),v_rs____),
file('LCL785-1.p',unknown),
[] ).
cnf(395,axiom,
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_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
file('LCL785-1.p',unknown),
[] ).
cnf(418,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_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
file('LCL785-1.p',unknown),
[] ).
cnf(423,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(rew,[status(thm),theory(equality)],[350,395]),
[iquote('0:Rew:350.0,395.0')] ).
cnf(436,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(rew,[status(thm),theory(equality)],[350,418]),
[iquote('0:Rew:350.0,418.0')] ).
cnf(441,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),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)],[369,436]),
[iquote('0:Rew:369.0,436.0')] ).
cnf(442,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(rew,[status(thm),theory(equality)],[394,441]),
[iquote('0:Rew:394.0,441.0')] ).
cnf(443,plain,
$false,
inference(mrr,[status(thm)],[442,423]),
[iquote('0:MRR:442.0,423.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL785-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.35 % Computer : n029.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 18:20:10 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.31/0.58
% 0.31/0.58 SPASS V 3.9
% 0.31/0.58 SPASS beiseite: Proof found.
% 0.31/0.58 % SZS status Theorem
% 0.31/0.58 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.31/0.58 SPASS derived 4 clauses, backtracked 0 clauses, performed 0 splits and kept 247 clauses.
% 0.31/0.58 SPASS allocated 76371 KBytes.
% 0.31/0.58 SPASS spent 0:00:00.19 on the problem.
% 0.31/0.58 0:00:00.07 for the input.
% 0.31/0.58 0:00:00.00 for the FLOTTER CNF translation.
% 0.31/0.58 0:00:00.00 for inferences.
% 0.31/0.58 0:00:00.00 for the backtracking.
% 0.31/0.58 0:00:00.05 for the reduction.
% 0.31/0.58
% 0.31/0.58
% 0.31/0.58 Here is a proof with depth 0, length 10 :
% 0.31/0.58 % SZS output start Refutation
% See solution above
% 0.31/0.58 Formulae used in the proof : cls_True_0 cls_foldl__Cons_0 cls_CHAINED_0 cls_CHAINED_0_01 cls_conjecture_0
% 0.31/0.58
%------------------------------------------------------------------------------