%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW209+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 : Thu Sep 24 03:07:26 PM UTC 2026
% Result : Theorem 0.37s 0.65s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 9 unt; 0 def)
% Number of atoms : 29 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 4 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 30 ( 28 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [B_m,B_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,B_m),hAPP(v_f____,B_n)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B_m,B_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,B_m),hAPP(v_ga____,B_n)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [V_xa_2,V_gb_2,V_fa_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2),V_gb_2),V_xa_2) = hAPP(V_fa_2,hAPP(V_gb_2,V_xa_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1161,conjecture,
! [B_m,B_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),B_m),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),B_n)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1162,negated_conjecture,
~ ! [B_m,B_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),B_m),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),B_n)) ),
inference(negated_conjecture,[status(cth)],[f1161]) ).
fof(f1166,plain,
! [B_m,B_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,B_m),hAPP(v_f____,B_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f1167,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,X0),hAPP(v_f____,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1166]) ).
fof(f1168,plain,
! [B_m,B_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,B_m),hAPP(v_ga____,B_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f1169,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,X0),hAPP(v_ga____,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1168]) ).
fof(f1173,plain,
! [X0,X1,X2,X3,X4,X5] : hAPP(hAPP(c_Fun_Ocomp(X0,X1,X2,X3),X4),X5) = hAPP(X3,hAPP(X4,X5)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f4488,plain,
? [B_m,B_n] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),B_m),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),B_n))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n) ),
inference(pre_NNF_transformation,[status(thm)],[f1162]) ).
fof(f4489,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK50_skl),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK51_skl))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK50_skl,sK51_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50_skl,sK51_skl]),skolemize(B_m,sK50_skl),skolemize(B_n,sK51_skl)],[f4488]) ).
fof(f4490,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK50_skl,sK51_skl),
inference(cnf_transformation,[status(thm)],[f4489]) ).
fof(f4491,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK50_skl),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK51_skl)),
inference(cnf_transformation,[status(thm)],[f4489]) ).
fof(f4697,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),sK50_skl),hAPP(v_f____,hAPP(v_ga____,sK51_skl))),
inference(backward_demodulation,[status(thm)],[f1173,f4491]) ).
fof(f4702,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,hAPP(v_ga____,sK50_skl)),hAPP(v_f____,hAPP(v_ga____,sK51_skl))),
inference(forward_demodulation,[status(thm)],[f1173,f4697]) ).
fof(f4707,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,sK50_skl),hAPP(v_ga____,sK51_skl)),
inference(resolution,[status(thm)],[f4702,f1167]) ).
fof(f4708,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK50_skl,sK51_skl),
inference(resolution,[status(thm)],[f4707,f1169]) ).
fof(f4709,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4708,f4490]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWW209+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n008.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 09:41:55 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.26/0.60 % Drodi V4.1.1
% 0.37/0.65 % Refutation found
% 0.37/0.65 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.37/0.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.40/0.70 % Elapsed time: 0.245376 seconds
% 0.40/0.70 % CPU time: 0.527225 seconds
% 0.40/0.70 % Total memory used: 141.450 MB
% 0.40/0.70 % Net memory used: 140.379 MB
%------------------------------------------------------------------------------