%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW293+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 : n009.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 39.08s 5.96s
% Output : CNFRefutation 39.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 18 unt; 0 def)
% Number of atoms : 63 ( 14 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 60 ( 25 ~; 18 |; 11 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 20 ( 20 usr; 10 con; 0-4 aty)
% Number of variables : 82 ( 75 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [V_Qa_2,V_c_2,V_Pa_2,V_n_2,T_b] :
( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2))
<=> ! [B_Z,B_s] :
( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
=> ! [B_s_H] :
( c_Natural_Oevaln(V_c_2,B_s,V_n_2,B_s_H)
=> hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s_H)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f191,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f202,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(f2207,axiom,
c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5205,conjecture,
c_Hoare__Mirabelle_Otriple__valid(t_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5206,negated_conjecture,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),
inference(negated_conjecture,[status(cth)],[f5205]) ).
fof(f5229,plain,
! [V_Qa_2,V_c_2,V_Pa_2,V_n_2,T_b] :
( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2))
<=> ! [B_Z,B_s] :
( ! [B_s_H] :
( hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s_H))
| ~ c_Natural_Oevaln(V_c_2,B_s,V_n_2,B_s_H) )
| ~ hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f5230,plain,
! [V_Qa_2,V_c_2,V_Pa_2,V_n_2,T_b] :
( ( ? [B_Z,B_s] :
( ? [B_s_H] :
( ~ hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s_H))
& c_Natural_Oevaln(V_c_2,B_s,V_n_2,B_s_H) )
& hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) )
| c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2)) )
& ( ! [B_Z,B_s] :
( ! [B_s_H] :
( hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s_H))
| ~ c_Natural_Oevaln(V_c_2,B_s,V_n_2,B_s_H) )
| ~ hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) )
| ~ c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2)) ) ),
inference(NNF_transformation,[status(thm)],[f5229]) ).
fof(f5231,plain,
( ! [V_Qa_2,V_c_2,V_Pa_2,V_n_2] :
( ? [B_Z,B_s] :
( ? [B_s_H] :
( ~ hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s_H))
& c_Natural_Oevaln(V_c_2,B_s,V_n_2,B_s_H) )
& hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) )
| ! [T_b] : c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2)) )
& ! [V_Qa_2,V_c_2,V_Pa_2,V_n_2] :
( ! [B_Z,B_s] :
( ! [B_s_H] :
( hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s_H))
| ~ c_Natural_Oevaln(V_c_2,B_s,V_n_2,B_s_H) )
| ~ hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) )
| ! [T_b] : ~ c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2)) ) ),
inference(miniscoping,[status(thm)],[f5230]) ).
fof(f5232,plain,
( ! [V_Qa_2,V_c_2,V_Pa_2,V_n_2] :
( ( ~ hBOOL(hAPP(hAPP(V_Qa_2,sK1_skl(V_n_2,V_Pa_2,V_c_2,V_Qa_2)),sK3_skl(V_n_2,V_Pa_2,V_c_2,V_Qa_2)))
& c_Natural_Oevaln(V_c_2,sK2_skl(V_n_2,V_Pa_2,V_c_2,V_Qa_2),V_n_2,sK3_skl(V_n_2,V_Pa_2,V_c_2,V_Qa_2))
& hBOOL(hAPP(hAPP(V_Pa_2,sK1_skl(V_n_2,V_Pa_2,V_c_2,V_Qa_2)),sK2_skl(V_n_2,V_Pa_2,V_c_2,V_Qa_2))) )
| ! [T_b] : c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2)) )
& ! [V_Qa_2,V_c_2,V_Pa_2,V_n_2] :
( ! [B_Z,B_s] :
( ! [B_s_H] :
( hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s_H))
| ~ c_Natural_Oevaln(V_c_2,B_s,V_n_2,B_s_H) )
| ~ hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) )
| ! [T_b] : ~ c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_c_2),V_Qa_2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(B_Z,sK1_skl(V_n_2,V_Pa_2,V_c_2,V_Qa_2)),skolemize(B_s,sK2_skl(V_n_2,V_Pa_2,V_c_2,V_Qa_2)),skolemize(B_s_H,sK3_skl(V_n_2,V_Pa_2,V_c_2,V_Qa_2))],[f5231]) ).
fof(f5235,plain,
! [X0,X1,X2,X3,X4] :
( c_Natural_Oevaln(X3,sK2_skl(X1,X2,X3,X4),X1,sK3_skl(X1,X2,X3,X4))
| c_Hoare__Mirabelle_Otriple__valid(X0,X1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X2),X3),X4)) ),
inference(cnf_transformation,[status(thm)],[f5232]) ).
fof(f5242,plain,
c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f5669,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)],[f191]) ).
fof(f5670,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,sK26_skl(V_P,V_s,V_n,V_s1),V_s1)
& V_n = hAPP(c_Nat_OSuc,sK26_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,[sK26_skl]),skolemize(B_n,sK26_skl(V_P,V_s,V_n,V_s1))],[f5669]) ).
fof(f5671,plain,
! [X0,X1,X2,X3] :
( X2 = hAPP(c_Nat_OSuc,sK26_skl(X0,X1,X2,X3))
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X0),X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f5670]) ).
fof(f5696,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f11757,plain,
c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[status(thm)],[f2207]) ).
fof(f19790,plain,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),
inference(cnf_transformation,[status(thm)],[f5206]) ).
fof(f20624,plain,
c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),sK2_skl(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_P,hAPP(c_Com_Ocom_OBODY,v_pn),v_Q),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK3_skl(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_P,hAPP(c_Com_Ocom_OBODY,v_pn),v_Q)),
inference(resolution,[status(thm)],[f5235,f19790]) ).
fof(f20711,plain,
c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),sK2_skl(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_P,hAPP(c_Com_Ocom_OBODY,v_pn),v_Q),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK3_skl(c_HOL_Obool_Obool__size(c_fTrue),v_P,hAPP(c_Com_Ocom_OBODY,v_pn),v_Q)),
inference(backward_demodulation,[status(thm)],[f5242,f20624]) ).
fof(f20721,plain,
c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),sK2_skl(c_HOL_Obool_Obool__size(c_fTrue),v_P,hAPP(c_Com_Ocom_OBODY,v_pn),v_Q),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK3_skl(c_HOL_Obool_Obool__size(c_fTrue),v_P,hAPP(c_Com_Ocom_OBODY,v_pn),v_Q)),
inference(forward_demodulation,[status(thm)],[f5242,f20711]) ).
fof(f20722,plain,
c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),sK2_skl(c_HOL_Obool_Obool__size(c_fTrue),v_P,hAPP(c_Com_Ocom_OBODY,v_pn),v_Q),c_HOL_Obool_Obool__size(c_fTrue),sK3_skl(c_HOL_Obool_Obool__size(c_fTrue),v_P,hAPP(c_Com_Ocom_OBODY,v_pn),v_Q)),
inference(forward_demodulation,[status(thm)],[f5242,f20721]) ).
fof(f28346,plain,
c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_OSuc,sK26_skl(v_pn,sK2_skl(c_HOL_Obool_Obool__size(c_fTrue),v_P,hAPP(c_Com_Ocom_OBODY,v_pn),v_Q),c_HOL_Obool_Obool__size(c_fTrue),sK3_skl(c_HOL_Obool_Obool__size(c_fTrue),v_P,hAPP(c_Com_Ocom_OBODY,v_pn),v_Q))),
inference(resolution,[status(thm)],[f5671,f20722]) ).
fof(f29368,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) != c_Orderings_Obot__class_Obot(tc_Nat_Onat),
inference(forward_demodulation,[status(thm)],[f11757,f5696]) ).
fof(f29369,plain,
c_HOL_Obool_Obool__size(c_fTrue) != c_Orderings_Obot__class_Obot(tc_Nat_Onat),
inference(paramodulation,[status(thm)],[f28346,f29368]) ).
fof(f31586,plain,
c_HOL_Obool_Obool__size(c_fTrue) = c_Orderings_Obot__class_Obot(tc_Nat_Onat),
inference(forward_demodulation,[status(thm)],[f11757,f5242]) ).
fof(f31587,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f31586,f29369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW293+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n009.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 09:46:12 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.80/1.06 % Drodi V4.1.1
% 39.08/5.96 % Refutation found
% 39.08/5.96 % SZS status Theorem for theBenchmark: Theorem is valid
% 39.08/5.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.23/6.43 % Elapsed time: 6.032043 seconds
% 6.23/6.43 % CPU time: 40.427338 seconds
% 6.23/6.43 % Total memory used: 1.056 GB
% 6.23/6.43 % Net memory used: 1.009 GB
%------------------------------------------------------------------------------