%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL825-1 : 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 : n018.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 08:50:11 AM UTC 2026
% Result : Unsatisfiable 32.66s 32.98s
% Output : Proof 32.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 21 ( 16 unt; 0 nHn; 16 RR)
% Number of literals : 32 ( 11 equ; 13 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 20 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_listsp_ONil_0,axiom,
c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a),
file('theBenchmark.p',cls_listsp_ONil_0) ).
cnf(cls_Nil__is__map__conv_1,axiom,
c_List_Olist_ONil(T_a) = c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a),
file('theBenchmark.p',cls_Nil__is__map__conv_1) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
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_106,axiom,
( c_List_Olistsp(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_List_Olistsp(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_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
inference(start,[status(thm),parent(0:0)],[cls_conjecture_0]) ).
cnf(t2,plain,
( c_List_Olist_ONil(tc_Lambda_OdB) != c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| tc_Lambda_OdB != tc_Lambda_OdB
| ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB)
| c_InductTermi_OIT != c_InductTermi_OIT
| c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(extension,[status(thm),parent(t1:1)],[equality_106]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ c_fequal(c_InductTermi_OIT,c_InductTermi_OIT,U_9785)
| c_InductTermi_OIT = c_InductTermi_OIT ),
inference(extension,[status(thm),parent(t2:2)],[cls_ATP__Linkup_Ofequal__imp__equal_0]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
c_fequal(c_InductTermi_OIT,c_InductTermi_OIT,U_9785),
inference(extension,[status(thm),parent(t4:2)],[cls_ATP__Linkup_Oequal__imp__fequal_0]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),
inference(extension,[status(thm),parent(t2:3)],[cls_listsp_ONil_0]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
( ~ c_fequal(tc_Lambda_OdB,tc_Lambda_OdB,U_9792)
| tc_Lambda_OdB = tc_Lambda_OdB ),
inference(extension,[status(thm),parent(t2:4)],[cls_ATP__Linkup_Ofequal__imp__equal_0]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:4]) ).
cnf(t12,plain,
c_fequal(tc_Lambda_OdB,tc_Lambda_OdB,U_9792),
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_List_Olist_ONil(tc_Lambda_OdB) = c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(extension,[status(thm),parent(t2:5)],[cls_Nil__is__map__conv_1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL825-1 : 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
% 0.08/0.34 % Computer : n018.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 15:57:10 UTC 2026
% 0.08/0.35 % CPUTime :
% 32.66/32.98 % SZS status Unsatisfiable for theBenchmark
% 32.66/32.98 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------