%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL856-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n016.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 03:01:06 PM UTC 2026
% Result : Unsatisfiable 0.23s 0.46s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of formulae : 31 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 114 ( 53 ~; 49 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 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 : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-3 aty)
% Number of variables : 56 ( 51 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_t_type,type,
v_t: $i ).
tff(c_InductTermi_OIT_type,type,
c_InductTermi_OIT: $i ).
tff(c_Type_Otyping_type,type,
c_Type_Otyping: ( $i * $i * $i ) > $o ).
tff(v_T_type,type,
v_T: $i ).
tff(v_e_type,type,
v_e: $i ).
tff(c_Wellfounded_Oaccp_type,type,
c_Wellfounded_Oaccp: ( $i * $i * $i ) > $o ).
tff(tc_Lambda_OdB_type,type,
tc_Lambda_OdB: $i ).
tff(c_Predicate_Oconversep_type,type,
c_Predicate_Oconversep: ( $i * $i * $i ) > $i ).
tff(c_Lambda_Obeta_type,type,
c_Lambda_Obeta: $i ).
tff(1,plain,
( c_Type_Otyping(v_e,v_t,v_T)
<=> c_Type_Otyping(v_e,v_t,v_T) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
c_Type_Otyping(v_e,v_t,v_T),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(3,plain,
c_Type_Otyping(v_e,v_t,v_T),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_T: $i,V_t: $i,V_e: $i] :
refl(( ( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) )
<=> ( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_T: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) )
<=> ! [V_T: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_T: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) )
<=> ! [V_T: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [V_T: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__implies__IT_0) ).
tff(8,plain,
! [V_T: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_T: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_T: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [V_T: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) )
| hBOOL(hAPP(c_InductTermi_OIT,v_t))
| ~ c_Type_Otyping(v_e,v_t,v_T) )
<=> ( ~ ! [V_T: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) )
| hBOOL(hAPP(c_InductTermi_OIT,v_t))
| ~ c_Type_Otyping(v_e,v_t,v_T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [V_T: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) )
| hBOOL(hAPP(c_InductTermi_OIT,v_t))
| ~ c_Type_Otyping(v_e,v_t,v_T) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [V_T: $i,V_t: $i,V_e: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,V_t))
| ~ c_Type_Otyping(V_e,V_t,V_T) )
| hBOOL(hAPP(c_InductTermi_OIT,v_t))
| ~ c_Type_Otyping(v_e,v_t,v_T) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_t)),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB)
<=> ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(17,plain,
~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
^ [V_t: $i] :
refl(( ( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) )
<=> ( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) )
<=> ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) )
<=> ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
^ [V_t: $i] :
rewrite(( ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) )
<=> ( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [V_t: $i] :
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) )
<=> ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [V_t: $i] :
( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB)
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT__implies__termi_0) ).
tff(24,plain,
! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) )
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB) )
<=> ( ~ ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) )
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) )
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [V_t: $i] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB) )
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_t))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),v_t,tc_Lambda_OdB) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
$false,
inference(unit_resolution,[status(thm)],[30,27,17,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL856-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.34 % Computer : n016.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
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 5 03:23:30 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.23/0.46 % SZS status Unsatisfiable
% 0.23/0.46 % SZS output start Proof
% See solution above
% 0.23/0.48 % E exiting
%------------------------------------------------------------------------------