%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL788-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n028.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 0.48s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 42 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 91 ( 54 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 82 ( 36 ~; 29 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 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 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-5 aty)
% Number of variables : 91 ( 81 !; 0 ?; 91 :)
% Comments :
%------------------------------------------------------------------------------
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_List_Ofoldr_type,type,
c_List_Ofoldr: ( $i * $i * $i * $i * $i ) > $i ).
tff(tc_Type_Otype_type,type,
tc_Type_Otype: $i ).
tff(v_T_H_____type,type,
v_T_H____: $i ).
tff(v_Ts_____type,type,
v_Ts____: $i ).
tff(c_Type_Otype_OFun_type,type,
c_Type_Otype_OFun: $i ).
tff(v_T_H_H_____type,type,
v_T_H_H____: $i ).
tff(v_i_____type,type,
v_i____: $i ).
tff(c_Type_Oshift_type,type,
c_Type_Oshift: ( $i * $i * $i * $i ) > $i ).
tff(v_T_____type,type,
v_T____: $i ).
tff(v_e_____type,type,
v_e____: $i ).
tff(c_Type_Otyping_type,type,
c_Type_Otyping: ( $i * $i * $i ) > $o ).
tff(c_Lambda_OdB_OVar_type,type,
c_Lambda_OdB_OVar: $i > $i ).
tff(v_n_____type,type,
v_n____: $i ).
tff(1,plain,
^ [V_x: $i,V_T: $i,T_a: $i,V_e: $i] :
refl(( ( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T )
<=> ( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_x: $i,V_T: $i,T_a: $i,V_e: $i] : ( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T )
<=> ! [V_x: $i,V_T: $i,T_a: $i,V_e: $i] : ( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_x: $i,V_T: $i,T_a: $i,V_e: $i] : ( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T )
<=> ! [V_x: $i,V_T: $i,T_a: $i,V_e: $i] : ( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_x: $i,V_T: $i,T_a: $i,V_e: $i] : ( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__eq_0) ).
tff(5,plain,
! [V_x: $i,V_T: $i,T_a: $i,V_e: $i] : ( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_x: $i,V_T: $i,T_a: $i,V_e: $i] : ( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_x: $i,V_T: $i,T_a: $i,V_e: $i] : ( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_x: $i,V_T: $i,T_a: $i,V_e: $i] : ( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T )
| ( hAPP(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_i____) = v_T____ ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
hAPP(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_i____) = v_T____,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( hAPP(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_i____) = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) )
<=> ( v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( ( v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) )
<=> ( hAPP(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_i____) = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ) ),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
( ( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) )
<=> ( hAPP(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_i____) != hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ) ),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,plain,
( ( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) )
<=> ( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
v_T____ != hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(15,plain,
v_T____ != hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
hAPP(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_i____) != hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(modus_ponens,[status(thm)],[15,12]) ).
tff(17,plain,
( ( v_n____ = v_i____ )
<=> ( v_n____ = v_i____ ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_True_0) ).
tff(19,plain,
v_n____ = v_i____,
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
v_i____ = v_n____,
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
c_Lambda_OdB_OVar(v_i____) = c_Lambda_OdB_OVar(v_n____),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
( c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
<=> c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
<=> c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) ),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
( c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
<=> c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_varT_0) ).
tff(26,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
inference(modus_ponens,[status(thm)],[26,23]) ).
tff(28,plain,
^ [V_i: $i,V_T: $i,V_e: $i] :
refl(( ( ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T)
| ( hAPP(V_e,V_i) = V_T ) )
<=> ( ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T)
| ( hAPP(V_e,V_i) = V_T ) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [V_i: $i,V_T: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T)
| ( hAPP(V_e,V_i) = V_T ) )
<=> ! [V_i: $i,V_T: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T)
| ( hAPP(V_e,V_i) = V_T ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [V_i: $i,V_T: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T)
| ( hAPP(V_e,V_i) = V_T ) )
<=> ! [V_i: $i,V_T: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T)
| ( hAPP(V_e,V_i) = V_T ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
^ [V_i: $i,V_T: $i,V_e: $i] :
rewrite(( ( ( hAPP(V_e,V_i) = V_T )
| ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T) )
<=> ( ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T)
| ( hAPP(V_e,V_i) = V_T ) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [V_i: $i,V_T: $i,V_e: $i] :
( ( hAPP(V_e,V_i) = V_T )
| ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T) )
<=> ! [V_i: $i,V_T: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T)
| ( hAPP(V_e,V_i) = V_T ) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,axiom,
! [V_i: $i,V_T: $i,V_e: $i] :
( ( hAPP(V_e,V_i) = V_T )
| ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
tff(34,plain,
! [V_i: $i,V_T: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T)
| ( hAPP(V_e,V_i) = V_T ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [V_i: $i,V_T: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T)
| ( hAPP(V_e,V_i) = V_T ) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
! [V_i: $i,V_T: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T)
| ( hAPP(V_e,V_i) = V_T ) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [V_i: $i,V_T: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T)
| ( hAPP(V_e,V_i) = V_T ) ),
inference(modus_ponens,[status(thm)],[36,29]) ).
tff(38,plain,
( ( ~ ! [V_i: $i,V_T: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T)
| ( hAPP(V_e,V_i) = V_T ) )
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ( hAPP(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_i____) = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ) )
<=> ( ~ ! [V_i: $i,V_T: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T)
| ( hAPP(V_e,V_i) = V_T ) )
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ( hAPP(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_i____) = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [V_i: $i,V_T: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T)
| ( hAPP(V_e,V_i) = V_T ) )
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ( hAPP(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_i____) = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [V_i: $i,V_T: $i,V_e: $i] :
( ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T)
| ( hAPP(V_e,V_i) = V_T ) )
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ( hAPP(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_i____) = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ( hAPP(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_i____) = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ) ),
inference(unit_resolution,[status(thm)],[40,37]) ).
tff(42,plain,
$false,
inference(unit_resolution,[status(thm)],[41,27,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL788-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.34 % Computer : n028.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 : Sun Sep 6 00:21:32 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.22/0.48 % SZS status Unsatisfiable
% 0.22/0.48 % SZS output start Proof
% See solution above
% 0.22/0.51 % E exiting
%------------------------------------------------------------------------------