%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL825-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n012.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 03:01:01 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.39s
% Output : Proof 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 27 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 14 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 9 ~; 2 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 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 : 50 ( 45 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_List_Olistsp_type,type,
c_List_Olistsp: ( $i * $i * $i ) > $o ).
tff(tc_Lambda_OdB_type,type,
tc_Lambda_OdB: $i ).
tff(c_List_Olist_ONil_type,type,
c_List_Olist_ONil: $i > $i ).
tff(c_InductTermi_OIT_type,type,
c_InductTermi_OIT: $i ).
tff(c_List_Omap_type,type,
c_List_Omap: ( $i * $i * $i * $i ) > $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_i_____type,type,
v_i____: $i ).
tff(c_COMBC_type,type,
c_COMBC: ( $i * $i * $i * $i ) > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(v_u_____type,type,
v_u____: $i ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(c_Lambda_Osubst_type,type,
c_Lambda_Osubst: $i ).
tff(1,plain,
^ [T_b: $i,V_f: $i,T_a: $i] :
refl(( ( c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a) )
<=> ( c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [T_b: $i,V_f: $i,T_a: $i] : ( c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a) )
<=> ! [T_b: $i,V_f: $i,T_a: $i] : ( c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [T_b: $i,V_f: $i,T_a: $i] : ( c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a) )
<=> ! [T_b: $i,V_f: $i,T_a: $i] : ( c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [T_b: $i,V_f: $i,T_a: $i] : ( c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__is__Nil__conv_1) ).
tff(5,plain,
! [T_b: $i,V_f: $i,T_a: $i] : ( c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [T_b: $i,V_f: $i,T_a: $i] : ( c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [T_b: $i,V_f: $i,T_a: $i] : ( c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [T_b: $i,V_f: $i,T_a: $i] : ( c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a) = c_List_Olist_ONil(T_a) )
| ( 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) = c_List_Olist_ONil(tc_Lambda_OdB) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
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) = c_List_Olist_ONil(tc_Lambda_OdB),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB)
<=> 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(monotonicity,[status(thm)],[10]) ).
tff(12,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)
<=> c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(symmetry,[status(thm)],[11]) ).
tff(13,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)
<=> ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,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)
<=> ~ 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(rewrite,[status(thm)],[]) ).
tff(15,axiom,
~ 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('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(16,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(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
^ [T_a: $i,V_A: $i] :
refl(( c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a)
<=> c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [T_a: $i,V_A: $i] : c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a)
<=> ! [T_a: $i,V_A: $i] : c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [T_a: $i,V_A: $i] : c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a)
<=> ! [T_a: $i,V_A: $i] : c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [T_a: $i,V_A: $i] : c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
tff(22,plain,
! [T_a: $i,V_A: $i] : c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [T_a: $i,V_A: $i] : c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [T_a: $i,V_A: $i] : c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ~ ! [T_a: $i,V_A: $i] : c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
$false,
inference(unit_resolution,[status(thm)],[26,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL825-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.01 % Command : run_E %s %d THM
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sat Sep 5 23:57:59 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.08/0.39 % SZS status Unsatisfiable
% 0.08/0.39 % SZS output start Proof
% See solution above
% 0.08/0.40 % E exiting
%------------------------------------------------------------------------------