%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL763-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n001.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 03:00:47 PM UTC 2026
% Result : Unsatisfiable 0.33s 0.56s
% Output : Proof 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 26 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 71 ( 33 ~; 28 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-5 aty)
% Number of variables : 54 ( 48 !; 0 ?; 54 :)
% 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(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_List_Ofoldl_type,type,
c_List_Ofoldl: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Lambda_OdB_OVar_type,type,
c_Lambda_OdB_OVar: $i > $i ).
tff(v_n_type,type,
v_n: $i ).
tff(c_Lambda_OdB_OApp_type,type,
c_Lambda_OdB_OApp: $i ).
tff(1,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
<=> ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(3,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_n: $i,V_rs: $i] :
refl(( ( ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB))) )
<=> ( ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB))) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_n: $i,V_rs: $i] :
( ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB))) )
<=> ! [V_n: $i,V_rs: $i] :
( ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_n: $i,V_rs: $i] :
( ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB))) )
<=> ! [V_n: $i,V_rs: $i] :
( ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [V_n: $i,V_rs: $i] :
rewrite(( ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB) )
<=> ( ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB))) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_n: $i,V_rs: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB) )
<=> ! [V_n: $i,V_rs: $i] :
( ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V_n: $i,V_rs: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
tff(10,plain,
! [V_n: $i,V_rs: $i] :
( ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V_n: $i,V_rs: $i] :
( ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V_n: $i,V_rs: $i] :
( ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_n: $i,V_rs: $i] :
( ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [V_n: $i,V_rs: $i] :
( ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB))) )
| ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) )
<=> ( ~ ! [V_n: $i,V_rs: $i] :
( ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB))) )
| ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [V_n: $i,V_rs: $i] :
( ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB))) )
| ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [V_n: $i,V_rs: $i] :
( ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB))) )
| ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),c_List_Olist_ONil(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(unit_resolution,[status(thm)],[16,13,3]) ).
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/sandbox2/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,
$false,
inference(unit_resolution,[status(thm)],[25,24,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL763-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 6 00:38:50 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.33/0.56 % SZS status Unsatisfiable
% 0.33/0.56 % SZS output start Proof
% See solution above
% 0.33/0.60 % E exiting
%------------------------------------------------------------------------------