%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL784-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n011.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 03:00:51 PM UTC 2026
% Result : Unsatisfiable 0.22s 0.53s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 49 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 66 ( 48 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 9 ~; 2 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 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; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-5 aty)
% Number of variables : 60 ( 54 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_u_____type,type,
v_u____: $i ).
tff(c_InductTermi_OIT_type,type,
c_InductTermi_OIT: $i ).
tff(v_i_____type,type,
v_i____: $i ).
tff(c_List_Ofoldl_type,type,
c_List_Ofoldl: ( $i * $i * $i * $i * $i ) > $i ).
tff(tc_Lambda_OdB_type,type,
tc_Lambda_OdB: $i ).
tff(v_rs_____type,type,
v_rs____: $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(c_Lambda_Osubst_type,type,
c_Lambda_Osubst: $i ).
tff(c_List_Olist_ONil_type,type,
c_List_Olist_ONil: $i > $i ).
tff(1,plain,
^ [T_b: $i,V_f: $i,V_a: $i,T_a: $i] :
refl(( ( c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a )
<=> ( c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [T_b: $i,V_f: $i,V_a: $i,T_a: $i] : ( c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a )
<=> ! [T_b: $i,V_f: $i,V_a: $i,T_a: $i] : ( c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [T_b: $i,V_f: $i,V_a: $i,T_a: $i] : ( c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a )
<=> ! [T_b: $i,V_f: $i,V_a: $i,T_a: $i] : ( c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [T_b: $i,V_f: $i,V_a: $i,T_a: $i] : ( c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
tff(5,plain,
! [T_b: $i,V_f: $i,V_a: $i,T_a: $i] : ( c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [T_b: $i,V_f: $i,V_a: $i,T_a: $i] : ( c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [T_b: $i,V_f: $i,V_a: $i,T_a: $i] : ( c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [T_b: $i,V_f: $i,V_a: $i,T_a: $i] : ( c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b) = V_a )
| ( 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) = c_Lambda_OdB_OVar(v_n____) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
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) = c_Lambda_OdB_OVar(v_n____),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( v_rs____ = c_List_Olist_ONil(tc_Lambda_OdB) )
<=> ( v_rs____ = c_List_Olist_ONil(tc_Lambda_OdB) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
v_rs____ = c_List_Olist_ONil(tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil_0) ).
tff(12,plain,
v_rs____ = c_List_Olist_ONil(tc_Lambda_OdB),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB) = 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(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OVar(v_n____),
inference(transitivity,[status(thm)],[13,9]) ).
tff(15,plain,
hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)) = hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_n____)),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____) = hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_n____)),v_u____),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_n____)),v_u____),v_i____),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_n____)),v_u____),v_i____) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____),
inference(symmetry,[status(thm)],[17]) ).
tff(19,plain,
( ( v_n____ = v_i____ )
<=> ( v_n____ = v_i____ ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_True_0) ).
tff(21,plain,
v_n____ = v_i____,
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
v_i____ = v_n____,
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
c_Lambda_OdB_OVar(v_i____) = c_Lambda_OdB_OVar(v_n____),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)) = hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_n____)),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____) = hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_n____)),v_u____),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____),v_i____) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_n____)),v_u____),v_i____),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
^ [V_u: $i,V_k: $i] :
refl(( ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u )
<=> ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [V_u: $i,V_k: $i] : ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u )
<=> ! [V_u: $i,V_k: $i] : ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [V_u: $i,V_k: $i] : ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u )
<=> ! [V_u: $i,V_k: $i] : ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
! [V_u: $i,V_k: $i] : ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).
tff(31,plain,
! [V_u: $i,V_k: $i] : ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [V_u: $i,V_k: $i] : ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [V_u: $i,V_k: $i] : ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ~ ! [V_u: $i,V_k: $i] : ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k) = V_u )
| ( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____),v_i____) = v_u____ ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____),v_i____) = v_u____,
inference(unit_resolution,[status(thm)],[34,33]) ).
tff(36,plain,
v_u____ = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_i____)),v_u____),v_i____),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
v_u____ = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____),
inference(transitivity,[status(thm)],[36,26,18]) ).
tff(38,plain,
hAPP(c_InductTermi_OIT,v_u____) = hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( hBOOL(hAPP(c_InductTermi_OIT,v_u____))
<=> hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)))
<=> hBOOL(hAPP(c_InductTermi_OIT,v_u____)) ),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)))
<=> ~ hBOOL(hAPP(c_InductTermi_OIT,v_u____)) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____)))
<=> ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(44,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
inference(modus_ponens,[status(thm)],[44,41]) ).
tff(46,plain,
( hBOOL(hAPP(c_InductTermi_OIT,v_u____))
<=> hBOOL(hAPP(c_InductTermi_OIT,v_u____)) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uIT_0) ).
tff(48,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
$false,
inference(unit_resolution,[status(thm)],[48,45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL784-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.07/0.35 % Computer : n011.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 4 23:14:00 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.22/0.53 % SZS status Unsatisfiable
% 0.22/0.53 % SZS output start Proof
% See solution above
% 0.22/0.56 % E exiting
%------------------------------------------------------------------------------