%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL849-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 01:08:35 PM UTC 2026
% Result : Unsatisfiable 62.63s 63.01s
% Output : Refutation 62.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 12 ( 7 unt; 0 nHn; 12 RR)
% Number of literals : 21 ( 0 equ; 14 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 11 con; 0-5 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
( ~ class_Orderings_Oorder(u)
| c_lessequals(v,v,u) ),
file('LCL849-1.p',unknown),
[] ).
cnf(41,axiom,
( ~ class_Orderings_Oorder(u)
| ~ c_lessequals(v,w,u)
| ~ c_lessequals(w,v,u)
| equal(v,w) ),
file('LCL849-1.p',unknown),
[] ).
cnf(650,axiom,
equal(c_List_Ofoldl(u,v,c_List_Olist_ONil(w),x,w),v),
file('LCL849-1.p',unknown),
[] ).
cnf(653,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('LCL849-1.p',unknown),
[] ).
cnf(684,axiom,
class_Orderings_Oorder(tc_nat),
file('LCL849-1.p',unknown),
[] ).
cnf(725,axiom,
~ equal(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)))),
file('LCL849-1.p',unknown),
[] ).
cnf(826,plain,
( ~ class_Orderings_Oorder(u)
| ~ c_lessequals(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat))),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),u)
| ~ c_lessequals(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat))),u) ),
inference(res,[status(thm),theory(equality)],[41,725]),
[iquote('0:Res:41.3,725.0')] ).
cnf(79464,plain,
equal(c_List_Ofoldl(u,v,c_List_Olist_OCons(w,c_List_Olist_ONil(x),x),y,x),hAPP(hAPP(u,v),w)),
inference(spr,[status(thm),theory(equality)],[653,650]),
[iquote('0:SpR:653.0,650.0')] ).
cnf(79632,plain,
( ~ class_Orderings_Oorder(u)
| ~ c_lessequals(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat))),u)
| ~ c_lessequals(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat))),u) ),
inference(rew,[status(thm),theory(equality)],[79464,826]),
[iquote('0:Rew:79464.0,826.2,79464.0,826.1')] ).
cnf(79633,plain,
( ~ class_Orderings_Oorder(u)
| ~ c_lessequals(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat))),u) ),
inference(obv,[status(thm),theory(equality)],[79632]),
[iquote('0:Obv:79632.1')] ).
cnf(79634,plain,
~ class_Orderings_Oorder(u),
inference(mrr,[status(thm)],[79633,6]),
[iquote('0:MRR:79633.1,6.1')] ).
cnf(79635,plain,
$false,
inference(unc,[status(thm)],[79634,684]),
[iquote('0:UnC:79634.0,684.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL849-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 5 04:36:55 UTC 2026
% 0.11/0.37 % CPUTime :
% 62.63/63.01
% 62.63/63.01 SPASS V 3.9
% 62.63/63.01 SPASS beiseite: Proof found.
% 62.63/63.01 % SZS status Theorem
% 62.63/63.01 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 62.63/63.01 SPASS derived 69297 clauses, backtracked 1339 clauses, performed 1 splits and kept 12734 clauses.
% 62.63/63.01 SPASS allocated 120849 KBytes.
% 62.63/63.01 SPASS spent 0:01:00.69 on the problem.
% 62.63/63.01 0:00:00.08 for the input.
% 62.63/63.01 0:00:00.00 for the FLOTTER CNF translation.
% 62.63/63.01 0:00:01.23 for inferences.
% 62.63/63.01 0:00:03.74 for the backtracking.
% 62.63/63.01 0:0:55.20 for the reduction.
% 62.63/63.01
% 62.63/63.01
% 62.63/63.01 Here is a proof with depth 1, length 12 :
% 62.63/63.01 % SZS output start Refutation
% See solution above
% 62.63/63.01 Formulae used in the proof : cls_order__eq__iff_0 cls_order__eq__iff_2 cls_foldl__Nil_0 cls_foldl__Cons_0 clsarity_nat__Orderings_Oorder cls_conjecture_0
% 62.63/63.01
%------------------------------------------------------------------------------