%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL748-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n020.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 03:00:45 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.45s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 38 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 79 ( 14 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 69 ( 31 ~; 24 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 43 ( 39 !; 0 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_InductTermi_OIT_type,type,
c_InductTermi_OIT: $i > $o ).
tff(c_Lambda_OdB_OAbs_type,type,
c_Lambda_OdB_OAbs: $i > $i ).
tff(c_Lambda_Olift_type,type,
c_Lambda_Olift: ( $i * $i ) > $i ).
tff(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(v_ia_type,type,
v_ia: $i ).
tff(v_r_type,type,
v_r: $i ).
tff(1,plain,
^ [V_k: $i,V_s: $i] :
refl(( ( c_Lambda_Olift(c_Lambda_OdB_OAbs(V_s),V_k) = c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) )
<=> ( c_Lambda_Olift(c_Lambda_OdB_OAbs(V_s),V_k) = c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_k: $i,V_s: $i] : ( c_Lambda_Olift(c_Lambda_OdB_OAbs(V_s),V_k) = c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) )
<=> ! [V_k: $i,V_s: $i] : ( c_Lambda_Olift(c_Lambda_OdB_OAbs(V_s),V_k) = c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_k: $i,V_s: $i] : ( c_Lambda_Olift(c_Lambda_OdB_OAbs(V_s),V_k) = c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) )
<=> ! [V_k: $i,V_s: $i] : ( c_Lambda_Olift(c_Lambda_OdB_OAbs(V_s),V_k) = c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_k: $i,V_s: $i] : ( c_Lambda_Olift(c_Lambda_OdB_OAbs(V_s),V_k) = c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I3_J_0) ).
tff(5,plain,
! [V_k: $i,V_s: $i] : ( c_Lambda_Olift(c_Lambda_OdB_OAbs(V_s),V_k) = c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_k: $i,V_s: $i] : ( c_Lambda_Olift(c_Lambda_OdB_OAbs(V_s),V_k) = c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_k: $i,V_s: $i] : ( c_Lambda_Olift(c_Lambda_OdB_OAbs(V_s),V_k) = c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_k: $i,V_s: $i] : ( c_Lambda_Olift(c_Lambda_OdB_OAbs(V_s),V_k) = c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) )
| ( c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),v_ia) = c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,c_HOL_Oplus__class_Oplus(v_ia,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),v_ia) = c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,c_HOL_Oplus__class_Oplus(v_ia,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,c_HOL_Oplus__class_Oplus(v_ia,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) = c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),v_ia),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,c_HOL_Oplus__class_Oplus(v_ia,c_HOL_Oone__class_Oone(tc_nat),tc_nat))))
<=> c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),v_ia)) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),v_ia))
<=> c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,c_HOL_Oplus__class_Oplus(v_ia,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))) ),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( ~ c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),v_ia))
<=> ~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,c_HOL_Oplus__class_Oplus(v_ia,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ~ c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),v_ia))
<=> ~ c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),v_ia)) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
~ c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),v_ia)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(16,plain,
~ c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),v_ia)),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,c_HOL_Oplus__class_Oplus(v_ia,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
^ [V_i: $i] :
refl(( c_InductTermi_OIT(c_Lambda_Olift(v_r,V_i))
<=> c_InductTermi_OIT(c_Lambda_Olift(v_r,V_i)) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [V_i: $i] : c_InductTermi_OIT(c_Lambda_Olift(v_r,V_i))
<=> ! [V_i: $i] : c_InductTermi_OIT(c_Lambda_Olift(v_r,V_i)) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_i: $i] : c_InductTermi_OIT(c_Lambda_Olift(v_r,V_i))
<=> ! [V_i: $i] : c_InductTermi_OIT(c_Lambda_Olift(v_r,V_i)) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [V_i: $i] : c_InductTermi_OIT(c_Lambda_Olift(v_r,V_i)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(22,plain,
! [V_i: $i] : c_InductTermi_OIT(c_Lambda_Olift(v_r,V_i)),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [V_i: $i] : c_InductTermi_OIT(c_Lambda_Olift(v_r,V_i)),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_i: $i] : c_InductTermi_OIT(c_Lambda_Olift(v_r,V_i)),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ~ ! [V_i: $i] : c_InductTermi_OIT(c_Lambda_Olift(v_r,V_i))
| c_InductTermi_OIT(c_Lambda_Olift(v_r,c_HOL_Oplus__class_Oplus(v_ia,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
c_InductTermi_OIT(c_Lambda_Olift(v_r,c_HOL_Oplus__class_Oplus(v_ia,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
^ [V_r: $i] :
refl(( ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) )
<=> ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [V_r: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) )
<=> ! [V_r: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [V_r: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) )
<=> ! [V_r: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
! [V_r: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lambda_0) ).
tff(31,plain,
! [V_r: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [V_r: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [V_r: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ( ~ ! [V_r: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) )
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,c_HOL_Oplus__class_Oplus(v_ia,c_HOL_Oone__class_Oone(tc_nat),tc_nat))))
| ~ c_InductTermi_OIT(c_Lambda_Olift(v_r,c_HOL_Oplus__class_Oplus(v_ia,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) )
<=> ( ~ ! [V_r: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) )
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,c_HOL_Oplus__class_Oplus(v_ia,c_HOL_Oone__class_Oone(tc_nat),tc_nat))))
| ~ c_InductTermi_OIT(c_Lambda_Olift(v_r,c_HOL_Oplus__class_Oplus(v_ia,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [V_r: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) )
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,c_HOL_Oplus__class_Oplus(v_ia,c_HOL_Oone__class_Oone(tc_nat),tc_nat))))
| ~ c_InductTermi_OIT(c_Lambda_Olift(v_r,c_HOL_Oplus__class_Oplus(v_ia,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [V_r: $i] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) )
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,c_HOL_Oplus__class_Oplus(v_ia,c_HOL_Oone__class_Oone(tc_nat),tc_nat))))
| ~ c_InductTermi_OIT(c_Lambda_Olift(v_r,c_HOL_Oplus__class_Oplus(v_ia,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,c_HOL_Oplus__class_Oplus(v_ia,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))),
inference(unit_resolution,[status(thm)],[36,33,26]) ).
tff(38,plain,
$false,
inference(unit_resolution,[status(thm)],[37,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL748-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.35 % Computer : n020.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 5 09:06:14 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.45 % SZS status Unsatisfiable
% 0.13/0.45 % SZS output start Proof
% See solution above
% 0.23/0.46 % E exiting
%------------------------------------------------------------------------------