%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW334+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 : n014.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 03:07:40 PM UTC 2026
% Result : Theorem 83.32s 12.01s
% Output : CNFRefutation 84.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 7 unt; 0 def)
% Number of atoms : 27 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 23 ( 11 ~; 8 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-2 aty)
% Number of variables : 29 ( 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [V_Qa_2,V_pn_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),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_2))
<=> c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5205,hypothesis,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_x),v_Procs)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5208,hypothesis,
! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,B_x))),v_Q(B_x))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5209,conjecture,
c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5210,negated_conjecture,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))),
inference(negated_conjecture,[status(cth)],[f5209]) ).
fof(f5214,plain,
! [V_Qa_2,V_pn_2,V_Pa_2,V_n_2,T_b] :
( ( ~ c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_2))
| c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_2)) )
& ( c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_2))
| ~ c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_2)) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f5215,plain,
( ! [V_Qa_2,V_pn_2,V_Pa_2,V_n_2,T_b] :
( ~ c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_2))
| c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_2)) )
& ! [V_Qa_2,V_pn_2,V_Pa_2,V_n_2,T_b] :
( c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_2))
| ~ c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_2)) ) ),
inference(miniscoping,[status(thm)],[f5214]) ).
fof(f5216,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_Hoare__Mirabelle_Otriple__valid(X0,X1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X3))),X4))
| c_Hoare__Mirabelle_Otriple__valid(X0,hAPP(c_Nat_OSuc,X1),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X2),hAPP(c_Com_Ocom_OBODY,X3)),X4)) ),
inference(cnf_transformation,[status(thm)],[f5215]) ).
fof(f19835,plain,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_x),v_Procs)),
inference(cnf_transformation,[status(thm)],[f5205]) ).
fof(f19840,plain,
! [B_x] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,B_x))),v_Q(B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs)) ),
inference(pre_NNF_transformation,[status(thm)],[f5208]) ).
fof(f19841,plain,
! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X0)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X0))),v_Q(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),v_Procs)) ),
inference(cnf_transformation,[status(thm)],[f19840]) ).
fof(f19842,plain,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))),
inference(cnf_transformation,[status(thm)],[f5210]) ).
fof(f20957,plain,
! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(X0)),hAPP(c_Com_Ocom_OBODY,X0)),v_Q(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),v_Procs)) ),
inference(resolution,[status(thm)],[f19841,f5216]) ).
fof(f25864,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_x),v_Procs)),
inference(resolution,[status(thm)],[f20957,f19842]) ).
fof(f29226,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f19835,f25864]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW334+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n014.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Mon Sep 21 09:47:50 UTC 2026
% 0.16/0.44 % CPUTime :
% 1.17/1.49 % Drodi V4.1.1
% 83.32/12.01 % Refutation found
% 83.32/12.01 % SZS status Theorem for theBenchmark: Theorem is valid
% 83.32/12.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 66.87/12.19 % Elapsed time: 11.726153 seconds
% 66.87/12.19 % CPU time: 84.956088 seconds
% 66.87/12.19 % Total memory used: 1.206 GB
% 66.87/12.19 % Net memory used: 1.183 GB
%------------------------------------------------------------------------------