%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL748-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 12:43:27 PM UTC 2026
% Result : Unsatisfiable 0.56s 0.81s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of clauses : 33 ( 19 unt; 0 nHn; 16 RR)
% Number of literals : 52 ( 37 equ; 20 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 44 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Suc__eq__plus1_0,axiom,
c_Suc(V_n) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ).
cnf(cls_lift_Osimps_I3_J_0,axiom,
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))) ).
cnf(cls_Lambda_0,axiom,
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
| ~ c_InductTermi_OIT(V_r) ) ).
cnf(cls_conjecture_1,negated_conjecture,
c_InductTermi_OIT(c_Lambda_Olift(v_r,V_i)) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),v_ia)) ).
cnf(refute_0_0,plain,
( ~ c_InductTermi_OIT(c_Lambda_Olift(v_r,V_i))
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,V_i))) ),
inference(subst,[],[cls_Lambda_0:[bind(V_r,$fot(c_Lambda_Olift(v_r,V_i)))]]) ).
cnf(refute_0_1,plain,
c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,V_i))),
inference(resolve,[$cnf( c_InductTermi_OIT(c_Lambda_Olift(v_r,V_i)) )],[cls_conjecture_1,refute_0_0]) ).
cnf(refute_0_2,plain,
c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,c_Suc(V_k)))),
inference(subst,[],[refute_0_1:[bind(V_i,$fot(c_Suc(V_k)))]]) ).
cnf(refute_0_3,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_4,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_5,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( c_Suc(V_n) != c_HOL_Oplus__class_Oplus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Oplus__class_Oplus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Suc(V_n) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(c_Suc(V_n))),bind(Y,$fot(c_HOL_Oplus__class_Oplus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))]]) ).
cnf(refute_0_7,plain,
c_HOL_Oplus__class_Oplus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Suc(V_n),
inference(resolve,[$cnf( $equal(c_Suc(V_n),c_HOL_Oplus__class_Oplus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) )],[cls_Suc__eq__plus1_0,refute_0_6]) ).
cnf(refute_0_8,plain,
c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Suc(V_k),
inference(subst,[],[refute_0_7:[bind(V_n,$fot(V_k))]]) ).
cnf(refute_0_9,plain,
c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),
introduced(tautology,[refl,[$fot(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))]]) ).
cnf(refute_0_10,plain,
( c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != c_Suc(V_k)
| c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) != c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))
| c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Olift(V_s,c_Suc(V_k)) ),
introduced(tautology,[equality,[$cnf( $equal(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) ),[1,1],$fot(c_Suc(V_k))]]) ).
cnf(refute_0_11,plain,
( c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != c_Suc(V_k)
| c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Olift(V_s,c_Suc(V_k)) ),
inference(resolve,[$cnf( $equal(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_Lambda_Olift(V_s,c_Suc(V_k)),
inference(resolve,[$cnf( $equal(c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Suc(V_k)) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) = c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
introduced(tautology,[refl,[$fot(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))))]]) ).
cnf(refute_0_14,plain,
( 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_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(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) != c_Lambda_Olift(V_s,c_Suc(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_OdB_OAbs(c_Lambda_Olift(V_s,c_Suc(V_k))) ),
introduced(tautology,[equality,[$cnf( $equal(c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))) ),[1,0],$fot(c_Lambda_Olift(V_s,c_Suc(V_k)))]]) ).
cnf(refute_0_15,plain,
( c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) != c_Lambda_Olift(V_s,c_Suc(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_OdB_OAbs(c_Lambda_Olift(V_s,c_Suc(V_k))) ),
inference(resolve,[$cnf( $equal(c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) = c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_Suc(V_k))),
inference(resolve,[$cnf( $equal(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_Lambda_Olift(V_s,c_Suc(V_k))) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
( c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) != c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_Suc(V_k)))
| c_Lambda_Olift(c_Lambda_OdB_OAbs(V_s),V_k) != c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))
| c_Lambda_Olift(c_Lambda_OdB_OAbs(V_s),V_k) = c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_Suc(V_k))) ),
introduced(tautology,[equality,[$cnf( $equal(c_Lambda_Olift(c_Lambda_OdB_OAbs(V_s),V_k),c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))) ),[1],$fot(c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_Suc(V_k))))]]) ).
cnf(refute_0_18,plain,
( 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_Suc(V_k))) ),
inference(resolve,[$cnf( $equal(c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_Suc(V_k)))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
c_Lambda_Olift(c_Lambda_OdB_OAbs(V_s),V_k) = c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_Suc(V_k))),
inference(resolve,[$cnf( $equal(c_Lambda_Olift(c_Lambda_OdB_OAbs(V_s),V_k),c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s,c_HOL_Oplus__class_Oplus(V_k,c_HOL_Oone__class_Oone(tc_nat),tc_nat)))) )],[cls_lift_Osimps_I3_J_0,refute_0_18]) ).
cnf(refute_0_20,plain,
c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),V_k) = c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,c_Suc(V_k))),
inference(subst,[],[refute_0_19:[bind(V_s,$fot(v_r))]]) ).
cnf(refute_0_21,plain,
( c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),V_k) != c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,c_Suc(V_k)))
| c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,c_Suc(V_k))) = c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),V_k) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),V_k))),bind(Y,$fot(c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,c_Suc(V_k)))))]]) ).
cnf(refute_0_22,plain,
c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,c_Suc(V_k))) = c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),V_k),
inference(resolve,[$cnf( $equal(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),V_k),c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,c_Suc(V_k)))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,c_Suc(V_k))) != c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),V_k)
| ~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,c_Suc(V_k))))
| c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),V_k)) ),
introduced(tautology,[equality,[$cnf( c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,c_Suc(V_k)))) ),[0],$fot(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),V_k))]]) ).
cnf(refute_0_24,plain,
( ~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,c_Suc(V_k))))
| c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),V_k)) ),
inference(resolve,[$cnf( $equal(c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,c_Suc(V_k))),c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),V_k)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),V_k)),
inference(resolve,[$cnf( c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,c_Suc(V_k)))) )],[refute_0_2,refute_0_24]) ).
cnf(refute_0_26,plain,
c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),v_ia)),
inference(subst,[],[refute_0_25:[bind(V_k,$fot(v_ia))]]) ).
cnf(refute_0_27,plain,
$false,
inference(resolve,[$cnf( c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),v_ia)) )],[refute_0_26,cls_conjecture_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL748-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 5 09:06:03 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.14/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.56/0.81 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.56/0.81
% 0.56/0.81 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.56/0.81
%------------------------------------------------------------------------------