%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL794-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 08:50:06 AM UTC 2026
% Result : Unsatisfiable 37.78s 38.05s
% Output : Proof 37.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 9
% Syntax : Number of clauses : 30 ( 21 unt; 0 nHn; 24 RR)
% Number of literals : 47 ( 11 equ; 19 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-5 aty)
% Number of variables : 31 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_lift__type_0,axiom,
( ~ c_Type_Otyping(V_e,V_t,V_T)
| c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),c_Lambda_Olift(V_t,V_i),V_T) ),
file('theBenchmark.p',cls_lift__type_0) ).
cnf(cls_App_0,axiom,
( ~ c_Type_Otyping(V_env,V_s,hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U))
| ~ c_Type_Otyping(V_env,V_t,V_T)
| c_Type_Otyping(V_env,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_U) ),
file('theBenchmark.p',cls_App_0) ).
cnf(cls_uT_H_0,axiom,
c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
file('theBenchmark.p',cls_uT_H_0) ).
cnf(cls_shift__eq_0,axiom,
hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T,
file('theBenchmark.p',cls_shift__eq_0) ).
cnf(cls_typing_OVar_0,axiom,
c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)),
file('theBenchmark.p',cls_typing_OVar_0) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
c_fequal(V_x,V_x,T_a),
file('theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
( ~ c_fequal(V_X,V_Y,T_a)
| V_X = V_Y ),
file('theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
cnf(equality_53,axiom,
( c_Type_Otyping(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Type_Otyping(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(start,[status(thm),parent(0:0)],[cls_conjecture_0]) ).
cnf(t2,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),v_T_H_H____)
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),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____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ),
inference(extension,[status(thm),parent(t1:1)],[cls_App_0]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),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____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) ),
inference(extension,[status(thm),parent(t2:2)],[cls_lift__type_0]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
inference(extension,[status(thm),parent(t4:2)],[cls_uT_H_0]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) != c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_HOL_Ozero__class_Ozero(tc_nat)) != v_T_H_H____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_HOL_Ozero__class_Ozero(tc_nat)))
| c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype) != c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype)
| c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),v_T_H_H____) ),
inference(extension,[status(thm),parent(t2:3)],[equality_53]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
( ~ c_fequal(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),U_8645)
| c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype) = c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype) ),
inference(extension,[status(thm),parent(t8:2)],[cls_ATP__Linkup_Ofequal__imp__equal_0]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
c_fequal(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),U_8645),
inference(extension,[status(thm),parent(t10:2)],[cls_ATP__Linkup_Oequal__imp__fequal_0]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(extension,[status(thm),parent(t8:3)],[cls_typing_OVar_0]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t8:3]) ).
cnf(t16,plain,
hAPP(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_HOL_Ozero__class_Ozero(tc_nat)) = v_T_H_H____,
inference(extension,[status(thm),parent(t8:4)],[cls_shift__eq_0]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t8:4]) ).
cnf(t18,plain,
( ~ c_fequal(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),U_8656)
| c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(extension,[status(thm),parent(t8:5)],[cls_ATP__Linkup_Ofequal__imp__equal_0]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t8:5]) ).
cnf(t20,plain,
c_fequal(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),U_8656),
inference(extension,[status(thm),parent(t18:2)],[cls_ATP__Linkup_Oequal__imp__fequal_0]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL794-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 15:55:15 UTC 2026
% 0.10/0.38 % CPUTime :
% 37.78/38.05 % SZS status Unsatisfiable for theBenchmark
% 37.78/38.05 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------