%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW220+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 03:07:27 PM UTC 2026
% Result : Theorem 4.94s 1.15s
% Output : CNFRefutation 4.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 9 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 55 ( 22 ~; 20 |; 7 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 50 ( 40 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
? [B_f] :
( ? [B_z] :
! [B_e] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e)
=> ? [B_N] :
! [B_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N),B_n))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(B_f,B_n)),B_z)),B_e) ) )
& c_SEQ_Osubseq(B_f) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1269,hypothesis,
! [B_f] :
( c_SEQ_Osubseq(B_f)
=> ( ? [B_z] :
! [B_e] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e)
=> ? [B_N] :
! [B_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N),B_n))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(B_f,B_n)),B_z)),B_e) ) )
=> v_thesis____ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1270,conjecture,
v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1271,negated_conjecture,
~ v_thesis____,
inference(negated_conjecture,[status(cth)],[f1270]) ).
fof(f1280,plain,
? [B_f] :
( ? [B_z] :
! [B_e] :
( ? [B_N] :
! [B_n] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(B_f,B_n)),B_z)),B_e)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N),B_n)) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e) )
& c_SEQ_Osubseq(B_f) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f1281,plain,
( ! [B_e] :
( ! [B_n] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(sK1_skl,B_n)),sK2_skl)),B_e)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK3_skl(B_e)),B_n)) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e) )
& c_SEQ_Osubseq(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(B_f,sK1_skl),skolemize(B_z,sK2_skl),skolemize(B_N,sK3_skl(B_e))],[f1280]) ).
fof(f1282,plain,
c_SEQ_Osubseq(sK1_skl),
inference(cnf_transformation,[status(thm)],[f1281]) ).
fof(f1283,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(sK1_skl,X1)),sK2_skl)),X0)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK3_skl(X0)),X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(cnf_transformation,[status(thm)],[f1281]) ).
fof(f4790,plain,
! [B_f] :
( v_thesis____
| ! [B_z] :
? [B_e] :
( ! [B_N] :
? [B_n] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(B_f,B_n)),B_z)),B_e)
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N),B_n)) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e) )
| ~ c_SEQ_Osubseq(B_f) ),
inference(pre_NNF_transformation,[status(thm)],[f1269]) ).
fof(f4791,plain,
! [B_f] :
( v_thesis____
| ! [B_z] :
( ! [B_N] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(B_f,sK79_skl(B_N,B_z,B_f))),B_z)),sK78_skl(B_z,B_f))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N),sK79_skl(B_N,B_z,B_f))) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK78_skl(B_z,B_f)) )
| ~ c_SEQ_Osubseq(B_f) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78_skl,sK79_skl]),skolemize(B_e,sK78_skl(B_z,B_f)),skolemize(B_n,sK79_skl(B_N,B_z,B_f))],[f4790]) ).
fof(f4792,plain,
! [X0,X1] :
( v_thesis____
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK78_skl(X1,X0))
| ~ c_SEQ_Osubseq(X0) ),
inference(cnf_transformation,[status(thm)],[f4791]) ).
fof(f4793,plain,
! [X0,X1,X2] :
( v_thesis____
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),sK79_skl(X1,X2,X0)))
| ~ c_SEQ_Osubseq(X0) ),
inference(cnf_transformation,[status(thm)],[f4791]) ).
fof(f4794,plain,
! [X0,X1,X2] :
( v_thesis____
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(X0,sK79_skl(X1,X2,X0))),X2)),sK78_skl(X2,X0))
| ~ c_SEQ_Osubseq(X0) ),
inference(cnf_transformation,[status(thm)],[f4791]) ).
fof(f4795,plain,
~ v_thesis____,
inference(cnf_transformation,[status(thm)],[f1271]) ).
fof(f5093,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(X0,sK79_skl(X1,X2,X0))),X2)),sK78_skl(X2,X0))
| ~ c_SEQ_Osubseq(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f4794,f4795]) ).
fof(f5094,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),sK79_skl(X1,X2,X0)))
| ~ c_SEQ_Osubseq(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f4793,f4795]) ).
fof(f5095,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK78_skl(X1,X0))
| ~ c_SEQ_Osubseq(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f4792,f4795]) ).
fof(f5117,plain,
! [X0,X1] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),sK79_skl(X0,X1,sK1_skl))),
inference(resolution,[status(thm)],[f1282,f5094]) ).
fof(f5118,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK78_skl(X0,sK1_skl)),
inference(resolution,[status(thm)],[f1282,f5095]) ).
fof(f5120,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(sK1_skl,sK79_skl(sK3_skl(X0),X1,sK1_skl))),sK2_skl)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(resolution,[status(thm)],[f1283,f5117]) ).
fof(f5121,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_g____(hAPP(sK1_skl,sK79_skl(sK3_skl(sK78_skl(X0,sK1_skl)),X1,sK1_skl))),sK2_skl)),sK78_skl(X0,sK1_skl)),
inference(resolution,[status(thm)],[f5120,f5118]) ).
fof(f5122,plain,
~ c_SEQ_Osubseq(sK1_skl),
inference(resolution,[status(thm)],[f5121,f5093]) ).
fof(f5123,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5122,f1282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW220+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n006.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 : Mon Sep 21 09:41:42 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.22/0.47 % Drodi V4.1.1
% 4.94/1.15 % Refutation found
% 4.94/1.15 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.94/1.15 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.94/1.19 % Elapsed time: 0.813895 seconds
% 4.94/1.19 % CPU time: 5.522434 seconds
% 4.94/1.19 % Total memory used: 271.601 MB
% 4.94/1.19 % Net memory used: 268.017 MB
%------------------------------------------------------------------------------