%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL849-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 : Thu Sep 24 08:50:15 AM UTC 2026
% Result : Unsatisfiable 46.45s 51.95s
% Output : Proof 46.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of clauses : 11 ( 9 unt; 0 nHn; 9 RR)
% Number of literals : 15 ( 12 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-5 aty)
% Number of variables : 13 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_foldl__Nil_0,axiom,
c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a,
file('theBenchmark.p',cls_foldl__Nil_0) ).
cnf(cls_foldl__Cons_0,axiom,
c_List_Ofoldl(V_f,V_a,c_List_Olist_OCons(V_x,V_xs,T_b),T_a,T_b) = c_List_Ofoldl(V_f,hAPP(hAPP(V_f,V_a),V_x),V_xs,T_a,T_b),
file('theBenchmark.p',cls_foldl__Cons_0) ).
cnf(cls_conjecture_0,negated_conjecture,
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('theBenchmark.p',cls_conjecture_0) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(t1,plain,
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))),
inference(start,[status(thm),parent(0:0)],[cls_conjecture_0]) ).
cnf(t2,plain,
( c_List_Ofoldl(c_Lambda_OdB_OApp,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_Olist_ONil(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)))
| 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) != c_List_Ofoldl(c_Lambda_OdB_OApp,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_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| 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))) ),
inference(extension,[status(thm),parent(t1:1)],[equality_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
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) = c_List_Ofoldl(c_Lambda_OdB_OApp,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_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(extension,[status(thm),parent(t2:2)],[cls_foldl__Cons_0]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,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_Olist_ONil(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))),
inference(extension,[status(thm),parent(t2:3)],[cls_foldl__Nil_0]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL849-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.56 % Computer : n006.cluster.edu
% 0.08/5.56 % Model : x86_64 x86_64
% 0.08/5.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.56 % Memory : 8046.5625MB
% 0.08/5.56 % OS : Linux 6.8.0-71-generic
% 0.08/5.56 % CPULimit : 300
% 0.08/5.56 % WCLimit : 300
% 0.08/5.56 % DateTime : Sat Sep 19 15:56:20 UTC 2026
% 0.08/5.56 % CPUTime :
% 46.45/51.95 % SZS status Unsatisfiable for theBenchmark
% 46.45/51.95 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------