%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW294+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 : n026.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 03:07:35 PM UTC 2026
% Result : Theorem 0.95s 1.97s
% Output : CNFRefutation 0.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 9 unt; 0 def)
% Number of atoms : 32 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 11 ~; 3 |; 6 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-4 aty)
% Number of variables : 30 ( 26 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f192,axiom,
! [V_s1,V_n,V_s,V_P] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_P),V_s,V_n,V_s1)
=> ~ ! [B_n] :
( V_n = hAPP(c_Nat_OSuc,B_n)
=> ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P)),V_s,B_n,V_s1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f203,axiom,
! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5207,conjecture,
! [B_Z,B_s] :
( v_P(B_Z,B_s)
=> ! [B_s_H] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),B_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B_s_H)
=> v_Q(B_Z,B_s_H) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5208,negated_conjecture,
~ ! [B_Z,B_s] :
( v_P(B_Z,B_s)
=> ! [B_s_H] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),B_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B_s_H)
=> v_Q(B_Z,B_s_H) ) ),
inference(negated_conjecture,[status(cth)],[f5207]) ).
fof(f5223,plain,
c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f5662,plain,
! [V_s1,V_n,V_s,V_P] :
( ? [B_n] :
( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P)),V_s,B_n,V_s1)
& V_n = hAPP(c_Nat_OSuc,B_n) )
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_P),V_s,V_n,V_s1) ),
inference(pre_NNF_transformation,[status(thm)],[f192]) ).
fof(f5663,plain,
! [V_s1,V_n,V_s,V_P] :
( ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P)),V_s,sK20_skl(V_P,V_s,V_n,V_s1),V_s1)
& V_n = hAPP(c_Nat_OSuc,sK20_skl(V_P,V_s,V_n,V_s1)) )
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_P),V_s,V_n,V_s1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl]),skolemize(B_n,sK20_skl(V_P,V_s,V_n,V_s1))],[f5662]) ).
fof(f5664,plain,
! [X0,X1,X2,X3] :
( X2 = hAPP(c_Nat_OSuc,sK20_skl(X0,X1,X2,X3))
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X0),X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f5663]) ).
fof(f5689,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f19786,plain,
? [B_Z,B_s] :
( ? [B_s_H] :
( ~ v_Q(B_Z,B_s_H)
& c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),B_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B_s_H) )
& v_P(B_Z,B_s) ),
inference(pre_NNF_transformation,[status(thm)],[f5208]) ).
fof(f19787,plain,
( ~ v_Q(sK494_skl,sK496_skl)
& c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),sK495_skl,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK496_skl)
& v_P(sK494_skl,sK495_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK494_skl,sK495_skl,sK496_skl]),skolemize(B_Z,sK494_skl),skolemize(B_s,sK495_skl),skolemize(B_s_H,sK496_skl)],[f19786]) ).
fof(f19789,plain,
c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),sK495_skl,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK496_skl),
inference(cnf_transformation,[status(thm)],[f19787]) ).
fof(f20573,plain,
c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),sK495_skl,c_HOL_Obool_Obool__size(c_fTrue),sK496_skl),
inference(backward_demodulation,[status(thm)],[f5223,f19789]) ).
fof(f20838,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) != c_HOL_Obool_Obool__size(c_fTrue),
inference(forward_demodulation,[status(thm)],[f5223,f5689]) ).
fof(f25033,plain,
c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_OSuc,sK20_skl(v_pn,sK495_skl,c_HOL_Obool_Obool__size(c_fTrue),sK496_skl)),
inference(resolution,[status(thm)],[f5664,f20573]) ).
fof(f25064,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f25033,f20838]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW294+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 09:48:51 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.79/1.05 % Drodi V4.1.1
% 0.95/1.97 % Refutation found
% 0.95/1.97 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.95/1.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.95/2.08 % Elapsed time: 1.691870 seconds
% 0.95/2.08 % CPU time: 7.968937 seconds
% 0.95/2.08 % Total memory used: 714.921 MB
% 0.95/2.08 % Net memory used: 708.688 MB
%------------------------------------------------------------------------------