%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW295+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 : n011.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 1.32s 1.76s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 23
% Syntax : Number of formulae : 109 ( 13 unt; 14 def)
% Number of atoms : 317 ( 78 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 350 ( 142 ~; 154 |; 24 &)
% ( 18 <=>; 11 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 15 prp; 0-4 aty)
% Number of functors : 21 ( 21 usr; 12 con; 0-4 aty)
% Number of variables : 136 ( 129 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [V_s1,V_n,V_s0,V_pn] :
( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn)),V_s0,V_n,V_s1)
=> c_Natural_Oevaln(c_Com_Ocom_OBODY(V_pn),V_s0,hAPP(c_Nat_OSuc,V_n),V_s1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [V_s1,V_n,V_s,V_P] :
( c_Natural_Oevaln(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/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [V_nat_H_2,V_nat_2] :
( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
<=> V_nat_2 = V_nat_H_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f116,axiom,
! [V_com2_2,V_com1_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1_2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f141,axiom,
! [V_na_2,V_m_2] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2)
<=> ( ( V_na_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f714,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f722,axiom,
! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5205,conjecture,
( ! [B_Z,B_s] :
( v_P(B_Z,B_s)
=> ! [B_s_H] :
( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),B_s,v_n,B_s_H)
=> v_Q(B_Z,B_s_H) ) )
<=> ! [B_Z,B_s] :
( v_P(B_Z,B_s)
=> ! [B_s_H] :
( c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),B_s,hAPP(c_Nat_OSuc,v_n),B_s_H)
=> v_Q(B_Z,B_s_H) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5206,negated_conjecture,
~ ( ! [B_Z,B_s] :
( v_P(B_Z,B_s)
=> ! [B_s_H] :
( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),B_s,v_n,B_s_H)
=> v_Q(B_Z,B_s_H) ) )
<=> ! [B_Z,B_s] :
( v_P(B_Z,B_s)
=> ! [B_s_H] :
( c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),B_s,hAPP(c_Nat_OSuc,v_n),B_s_H)
=> v_Q(B_Z,B_s_H) ) ) ),
inference(negated_conjecture,[status(cth)],[f5205]) ).
fof(f5210,plain,
! [V_s1,V_n,V_s0,V_pn] :
( c_Natural_Oevaln(c_Com_Ocom_OBODY(V_pn),V_s0,hAPP(c_Nat_OSuc,V_n),V_s1)
| ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn)),V_s0,V_n,V_s1) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f5211,plain,
! [X0,X1,X2,X3] :
( c_Natural_Oevaln(c_Com_Ocom_OBODY(X0),X1,hAPP(c_Nat_OSuc,X2),X3)
| ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X0)),X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f5210]) ).
fof(f5218,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(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f5219,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,sK1_skl(V_P,V_s,V_n,V_s1),V_s1)
& V_n = hAPP(c_Nat_OSuc,sK1_skl(V_P,V_s,V_n,V_s1)) )
| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(V_P),V_s,V_n,V_s1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(B_n,sK1_skl(V_P,V_s,V_n,V_s1))],[f5218]) ).
fof(f5220,plain,
! [X0,X1,X2,X3] :
( X2 = hAPP(c_Nat_OSuc,sK1_skl(X0,X1,X2,X3))
| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(X0),X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f5219]) ).
fof(f5221,plain,
! [X0,X1,X2,X3] :
( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X0)),X1,sK1_skl(X0,X1,X2,X3),X3)
| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(X0),X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f5219]) ).
fof(f5228,plain,
! [V_nat_H_2,V_nat_2] :
( ( V_nat_2 != V_nat_H_2
| hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) )
& ( V_nat_2 = V_nat_H_2
| hAPP(c_Nat_OSuc,V_nat_2) != hAPP(c_Nat_OSuc,V_nat_H_2) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f5229,plain,
( ! [V_nat_H_2,V_nat_2] :
( V_nat_2 != V_nat_H_2
| hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) )
& ! [V_nat_H_2,V_nat_2] :
( V_nat_2 = V_nat_H_2
| hAPP(c_Nat_OSuc,V_nat_2) != hAPP(c_Nat_OSuc,V_nat_H_2) ) ),
inference(miniscoping,[status(thm)],[f5228]) ).
fof(f5230,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Nat_OSuc,X0) != hAPP(c_Nat_OSuc,X1) ),
inference(cnf_transformation,[status(thm)],[f5229]) ).
fof(f5364,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f5490,plain,
! [X0,X1,X2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X0,X1,X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f5555,plain,
! [V_na_2,V_m_2] :
( ( ( ( V_na_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2) )
& ( ( V_na_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2) ) ),
inference(NNF_transformation,[status(thm)],[f141]) ).
fof(f5556,plain,
( ! [V_na_2,V_m_2] :
( ( ( V_na_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2) )
& ! [V_na_2,V_m_2] :
( ( V_na_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2) ) ),
inference(miniscoping,[status(thm)],[f5555]) ).
fof(f5559,plain,
! [X0,X1] :
( X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1) ),
inference(cnf_transformation,[status(thm)],[f5556]) ).
fof(f7279,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[status(thm)],[f714]) ).
fof(f7302,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),
inference(cnf_transformation,[status(thm)],[f722]) ).
fof(f19777,plain,
( ! [B_Z,B_s] :
( ! [B_s_H] :
( v_Q(B_Z,B_s_H)
| ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),B_s,v_n,B_s_H) )
| ~ v_P(B_Z,B_s) )
<~> ! [B_Z,B_s] :
( ! [B_s_H] :
( v_Q(B_Z,B_s_H)
| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),B_s,hAPP(c_Nat_OSuc,v_n),B_s_H) )
| ~ v_P(B_Z,B_s) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5206]) ).
fof(f19778,plain,
( ( ? [B_Z,B_s] :
( ? [B_s_H] :
( ~ v_Q(B_Z,B_s_H)
& c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),B_s,hAPP(c_Nat_OSuc,v_n),B_s_H) )
& v_P(B_Z,B_s) )
| ? [B_Z,B_s] :
( ? [B_s_H] :
( ~ v_Q(B_Z,B_s_H)
& c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),B_s,v_n,B_s_H) )
& v_P(B_Z,B_s) ) )
& ( ! [B_Z,B_s] :
( ! [B_s_H] :
( v_Q(B_Z,B_s_H)
| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),B_s,hAPP(c_Nat_OSuc,v_n),B_s_H) )
| ~ v_P(B_Z,B_s) )
| ! [B_Z,B_s] :
( ! [B_s_H] :
( v_Q(B_Z,B_s_H)
| ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),B_s,v_n,B_s_H) )
| ~ v_P(B_Z,B_s) ) ) ),
inference(NNF_transformation,[status(thm)],[f19777]) ).
fof(f19779,plain,
( ( ( ~ v_Q(sK491_skl,sK493_skl)
& c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),sK492_skl,hAPP(c_Nat_OSuc,v_n),sK493_skl)
& v_P(sK491_skl,sK492_skl) )
| ( ~ v_Q(sK488_skl,sK490_skl)
& c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),sK489_skl,v_n,sK490_skl)
& v_P(sK488_skl,sK489_skl) ) )
& ( ! [B_Z,B_s] :
( ! [B_s_H] :
( v_Q(B_Z,B_s_H)
| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),B_s,hAPP(c_Nat_OSuc,v_n),B_s_H) )
| ~ v_P(B_Z,B_s) )
| ! [B_Z,B_s] :
( ! [B_s_H] :
( v_Q(B_Z,B_s_H)
| ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),B_s,v_n,B_s_H) )
| ~ v_P(B_Z,B_s) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK488_skl,sK489_skl,sK490_skl,sK491_skl,sK492_skl,sK493_skl]),skolemize(B_Z,sK488_skl),skolemize(B_s,sK489_skl),skolemize(B_s_H,sK490_skl),skolemize(B_Z,sK491_skl),skolemize(B_s,sK492_skl),skolemize(B_s_H,sK493_skl)],[f19778]) ).
fof(f19780,plain,
! [X0,X1,X2,X3,X4,X5] :
( v_Q(X3,X5)
| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),X4,hAPP(c_Nat_OSuc,v_n),X5)
| ~ v_P(X3,X4)
| v_Q(X0,X2)
| ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),X1,v_n,X2)
| ~ v_P(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f19779]) ).
fof(f19781,plain,
( v_P(sK491_skl,sK492_skl)
| v_P(sK488_skl,sK489_skl) ),
inference(cnf_transformation,[status(thm)],[f19779]) ).
fof(f19782,plain,
( c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),sK492_skl,hAPP(c_Nat_OSuc,v_n),sK493_skl)
| v_P(sK488_skl,sK489_skl) ),
inference(cnf_transformation,[status(thm)],[f19779]) ).
fof(f19783,plain,
( ~ v_Q(sK491_skl,sK493_skl)
| v_P(sK488_skl,sK489_skl) ),
inference(cnf_transformation,[status(thm)],[f19779]) ).
fof(f19784,plain,
( v_P(sK491_skl,sK492_skl)
| c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),sK489_skl,v_n,sK490_skl) ),
inference(cnf_transformation,[status(thm)],[f19779]) ).
fof(f19785,plain,
( c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),sK492_skl,hAPP(c_Nat_OSuc,v_n),sK493_skl)
| c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),sK489_skl,v_n,sK490_skl) ),
inference(cnf_transformation,[status(thm)],[f19779]) ).
fof(f19786,plain,
( ~ v_Q(sK491_skl,sK493_skl)
| c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),sK489_skl,v_n,sK490_skl) ),
inference(cnf_transformation,[status(thm)],[f19779]) ).
fof(f19787,plain,
( v_P(sK491_skl,sK492_skl)
| ~ v_Q(sK488_skl,sK490_skl) ),
inference(cnf_transformation,[status(thm)],[f19779]) ).
fof(f19788,plain,
( c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),sK492_skl,hAPP(c_Nat_OSuc,v_n),sK493_skl)
| ~ v_Q(sK488_skl,sK490_skl) ),
inference(cnf_transformation,[status(thm)],[f19779]) ).
fof(f19789,plain,
( ~ v_Q(sK491_skl,sK493_skl)
| ~ v_Q(sK488_skl,sK490_skl) ),
inference(cnf_transformation,[status(thm)],[f19779]) ).
fof(f20091,definition,
( sQ5_spl
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f20092,plain,
( ~ sQ5_spl
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(component_clause,[status(thm)],[f20091]) ).
fof(f20122,definition,
! [X0,X1,X2] :
( sQ13_spl
<=> ( v_Q(X0,X2)
| ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),X1,v_n,X2)
| ~ v_P(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f20123,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| v_Q(X0,X2)
| ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),X1,v_n,X2)
| ~ v_P(X0,X1) ),
inference(component_clause,[status(thm)],[f20122]) ).
fof(f20125,definition,
! [X3,X4,X5] :
( sQ14_spl
<=> ( v_Q(X3,X5)
| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),X4,hAPP(c_Nat_OSuc,v_n),X5)
| ~ v_P(X3,X4) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f20126,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| v_Q(X0,X2)
| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),X1,hAPP(c_Nat_OSuc,v_n),X2)
| ~ v_P(X0,X1) ),
inference(component_clause,[status(thm)],[f20125]) ).
fof(f20128,plain,
( sQ14_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f19780,f20122,f20125]) ).
fof(f20129,definition,
( sQ15_spl
<=> v_P(sK488_skl,sK489_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f20130,plain,
( ~ sQ15_spl
| v_P(sK488_skl,sK489_skl) ),
inference(component_clause,[status(thm)],[f20129]) ).
fof(f20132,definition,
( sQ16_spl
<=> v_P(sK491_skl,sK492_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f20133,plain,
( ~ sQ16_spl
| v_P(sK491_skl,sK492_skl) ),
inference(component_clause,[status(thm)],[f20132]) ).
fof(f20135,plain,
( sQ16_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f19781,f20129,f20132]) ).
fof(f20136,definition,
( sQ17_spl
<=> c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),sK492_skl,hAPP(c_Nat_OSuc,v_n),sK493_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f20137,plain,
( ~ sQ17_spl
| c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),sK492_skl,hAPP(c_Nat_OSuc,v_n),sK493_skl) ),
inference(component_clause,[status(thm)],[f20136]) ).
fof(f20139,plain,
( sQ17_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f19782,f20129,f20136]) ).
fof(f20140,definition,
( sQ18_spl
<=> v_Q(sK491_skl,sK493_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f20142,plain,
( sQ18_spl
| ~ v_Q(sK491_skl,sK493_skl) ),
inference(component_clause,[status(thm)],[f20140]) ).
fof(f20143,plain,
( ~ sQ18_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f19783,f20129,f20140]) ).
fof(f20144,definition,
( sQ19_spl
<=> c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),sK489_skl,v_n,sK490_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f20145,plain,
( ~ sQ19_spl
| c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),sK489_skl,v_n,sK490_skl) ),
inference(component_clause,[status(thm)],[f20144]) ).
fof(f20147,plain,
( sQ16_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f19784,f20144,f20132]) ).
fof(f20148,plain,
( sQ17_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f19785,f20144,f20136]) ).
fof(f20149,plain,
( ~ sQ18_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f19786,f20144,f20140]) ).
fof(f20150,definition,
( sQ20_spl
<=> v_Q(sK488_skl,sK490_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f20152,plain,
( sQ20_spl
| ~ v_Q(sK488_skl,sK490_skl) ),
inference(component_clause,[status(thm)],[f20150]) ).
fof(f20153,plain,
( sQ16_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f19787,f20150,f20132]) ).
fof(f20154,plain,
( sQ17_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f19788,f20150,f20136]) ).
fof(f20155,plain,
( ~ sQ18_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f19789,f20150,f20140]) ).
fof(f20654,plain,
! [X0] :
( sQ20_spl
| ~ sQ13_spl
| ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),X0,v_n,sK490_skl)
| ~ v_P(sK488_skl,X0) ),
inference(resolution,[status(thm)],[f20123,f20152]) ).
fof(f20659,plain,
( ~ sQ15_spl
| sQ20_spl
| ~ sQ13_spl
| ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),sK489_skl,v_n,sK490_skl) ),
inference(resolution,[status(thm)],[f20654,f20130]) ).
fof(f20660,plain,
( ~ sQ15_spl
| sQ20_spl
| ~ sQ13_spl
| ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f20659,f20145]) ).
fof(f20661,plain,
( ~ sQ15_spl
| sQ20_spl
| ~ sQ13_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f20660]) ).
fof(f20666,plain,
( ~ sQ17_spl
| hAPP(c_Nat_OSuc,v_n) = hAPP(c_Nat_OSuc,sK1_skl(v_pn,sK492_skl,hAPP(c_Nat_OSuc,v_n),sK493_skl)) ),
inference(resolution,[status(thm)],[f20137,f5220]) ).
fof(f20667,plain,
! [X0] :
( sQ18_spl
| ~ sQ14_spl
| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),X0,hAPP(c_Nat_OSuc,v_n),sK493_skl)
| ~ v_P(sK491_skl,X0) ),
inference(resolution,[status(thm)],[f20126,f20142]) ).
fof(f20668,plain,
! [X0] :
( sQ20_spl
| ~ sQ14_spl
| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),X0,hAPP(c_Nat_OSuc,v_n),sK490_skl)
| ~ v_P(sK488_skl,X0) ),
inference(resolution,[status(thm)],[f20126,f20152]) ).
fof(f20671,plain,
( ~ sQ17_spl
| v_n = sK1_skl(v_pn,sK492_skl,hAPP(c_Nat_OSuc,v_n),sK493_skl) ),
inference(resolution,[status(thm)],[f20666,f5230]) ).
fof(f20686,plain,
( ~ sQ16_spl
| sQ18_spl
| ~ sQ14_spl
| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),sK492_skl,hAPP(c_Nat_OSuc,v_n),sK493_skl) ),
inference(resolution,[status(thm)],[f20667,f20133]) ).
fof(f20687,plain,
( ~ sQ16_spl
| sQ18_spl
| ~ sQ14_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f20686,f20137]) ).
fof(f20688,plain,
( ~ sQ16_spl
| sQ18_spl
| ~ sQ14_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f20687]) ).
fof(f20694,plain,
( ~ sQ17_spl
| c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),sK492_skl,v_n,sK493_skl)
| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),sK492_skl,hAPP(c_Nat_OSuc,v_n),sK493_skl) ),
inference(paramodulation,[status(thm)],[f20671,f5221]) ).
fof(f20695,definition,
( sQ21_spl
<=> c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),sK492_skl,v_n,sK493_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f20696,plain,
( ~ sQ21_spl
| c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),sK492_skl,v_n,sK493_skl) ),
inference(component_clause,[status(thm)],[f20695]) ).
fof(f20698,plain,
( sQ21_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f20694,f20136,f20695]) ).
fof(f20712,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(paramodulation,[status(thm)],[f7279,f5364]) ).
fof(f20713,plain,
! [X0] :
( X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,X0) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f7279,f5230]) ).
fof(f20720,plain,
! [X0,X1,X2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X0,X1,X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2))),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[status(thm)],[f7279,f5490]) ).
fof(f20740,plain,
( ~ sQ15_spl
| sQ20_spl
| ~ sQ14_spl
| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),sK489_skl,hAPP(c_Nat_OSuc,v_n),sK490_skl) ),
inference(resolution,[status(thm)],[f20668,f20130]) ).
fof(f20742,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(paramodulation,[status(thm)],[f7279,f20713]) ).
fof(f20743,definition,
( sQ22_spl
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f20745,plain,
( sQ22_spl
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(component_clause,[status(thm)],[f20743]) ).
fof(f20746,definition,
( sQ23_spl
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f20749,plain,
( sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f20742,f20743,f20746]) ).
fof(f20750,plain,
( sQ22_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f20745]) ).
fof(f20751,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f20750]) ).
fof(f20834,plain,
! [X0] :
( sQ18_spl
| ~ sQ13_spl
| ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),X0,v_n,sK493_skl)
| ~ v_P(sK491_skl,X0) ),
inference(resolution,[status(thm)],[f20123,f20142]) ).
fof(f20838,plain,
! [X0,X1] :
( X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1) ),
inference(forward_demodulation,[status(thm)],[f7279,f5559]) ).
fof(f20840,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X0,X1,X2)) ),
inference(paramodulation,[status(thm)],[f20720,f20838]) ).
fof(f20844,definition,
! [X0,X1,X2] :
( sQ25_spl
<=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(X0,X1,X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f20847,plain,
( sQ5_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f20840,f20844,f20091]) ).
fof(f20918,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f20092,f20712]) ).
fof(f20919,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f20918]) ).
fof(f20922,plain,
( ~ sQ16_spl
| sQ18_spl
| ~ sQ13_spl
| ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),sK492_skl,v_n,sK493_skl) ),
inference(resolution,[status(thm)],[f20834,f20133]) ).
fof(f20930,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X0) ),
inference(paramodulation,[status(thm)],[f7302,f20838]) ).
fof(f20941,definition,
! [X0] :
( sQ27_spl
<=> ( X0 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f20944,plain,
( sQ5_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f20930,f20941,f20091]) ).
fof(f21013,plain,
( ~ sQ16_spl
| sQ18_spl
| ~ sQ13_spl
| ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f20922,f20696]) ).
fof(f21014,plain,
( ~ sQ16_spl
| sQ18_spl
| ~ sQ13_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f21013]) ).
fof(f21026,plain,
( ~ sQ15_spl
| sQ20_spl
| ~ sQ14_spl
| ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)),sK489_skl,v_n,sK490_skl) ),
inference(resolution,[status(thm)],[f20740,f5211]) ).
fof(f21028,plain,
( ~ sQ15_spl
| sQ20_spl
| ~ sQ14_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f21026,f20144,f20125,f20150,f20129]) ).
fof(f21029,plain,
$false,
inference(sat_refutation,[status(thm)],[f20128,f20135,f20139,f20143,f20147,f20148,f20149,f20153,f20154,f20155,f20661,f20688,f20698,f20749,f20751,f20847,f20919,f20944,f21014,f21028]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW295+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n011.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 09:45:56 UTC 2026
% 0.19/0.45 % CPUTime :
% 1.17/1.48 % Drodi V4.1.1
% 1.32/1.76 % Refutation found
% 1.32/1.76 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.32/1.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.34/1.91 % Elapsed time: 1.430809 seconds
% 1.34/1.91 % CPU time: 3.286508 seconds
% 1.34/1.91 % Total memory used: 660.085 MB
% 1.34/1.91 % Net memory used: 654.188 MB
%------------------------------------------------------------------------------