%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW374+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 : n012.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 03:07:44 PM UTC 2026
% Result : Theorem 1.75s 6.25s
% Output : CNFRefutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 22 unt; 0 def)
% Number of atoms : 94 ( 37 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 75 ( 32 ~; 32 |; 5 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 82 ( 76 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [V_A_2,V_x_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
<=> hBOOL(hAPP(V_A_2,V_x_2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [V_b,V_pn] :
( c_Com_OWT__bodies
=> ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b)
=> hBOOL(hAPP(c_Com_OWT,V_b)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [V_a_2] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(V_a_2)))
<=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [V_m_2,T_b,V_a_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2)))
=> ? [B_b] : hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),B_b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [V_pn] :
( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom)
=> hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(V_pn))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5246,hypothesis,
c_Com_OWT__bodies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5248,hypothesis,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5249,conjecture,
hBOOL(hAPP(c_Com_OWT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5250,negated_conjecture,
~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)))),
inference(negated_conjecture,[status(cth)],[f5249]) ).
fof(f5260,plain,
! [V_A_2,V_x_2,T_a] :
( ( ~ hBOOL(hAPP(V_A_2,V_x_2))
| hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) )
& ( hBOOL(hAPP(V_A_2,V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f5261,plain,
( ! [V_A_2,V_x_2] :
( ~ hBOOL(hAPP(V_A_2,V_x_2))
| ! [T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) )
& ! [V_A_2,V_x_2] :
( hBOOL(hAPP(V_A_2,V_x_2))
| ! [T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ),
inference(miniscoping,[status(thm)],[f5260]) ).
fof(f5262,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X1),X2)) ),
inference(cnf_transformation,[status(thm)],[f5261]) ).
fof(f5263,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(hAPP(c_member(X0),X1),X2)) ),
inference(cnf_transformation,[status(thm)],[f5261]) ).
fof(f5281,plain,
! [V_b,V_pn] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b)
| ~ c_Com_OWT__bodies ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f5282,plain,
( ! [V_b] :
( hBOOL(hAPP(c_Com_OWT,V_b))
| ! [V_pn] : hAPP(c_Com_Obody,V_pn) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) )
| ~ c_Com_OWT__bodies ),
inference(miniscoping,[status(thm)],[f5281]) ).
fof(f5283,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Com_OWT,X1))
| hAPP(c_Com_Obody,X0) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1)
| ~ c_Com_OWT__bodies ),
inference(cnf_transformation,[status(thm)],[f5282]) ).
fof(f5331,plain,
! [X0,X1] : hAPP(c_Option_Othe(X0),hAPP(c_Option_Ooption_OSome(X0),X1)) = X1,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f5332,plain,
! [V_a_2] :
( ( ! [B_y] : hAPP(c_Com_Obody,V_a_2) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y)
| hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(V_a_2))) )
& ( ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y)
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(V_a_2))) ) ),
inference(NNF_transformation,[status(thm)],[f22]) ).
fof(f5333,plain,
( ! [V_a_2] :
( ! [B_y] : hAPP(c_Com_Obody,V_a_2) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y)
| hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(V_a_2))) )
& ! [V_a_2] :
( ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y)
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(V_a_2))) ) ),
inference(miniscoping,[status(thm)],[f5332]) ).
fof(f5334,plain,
( ! [V_a_2] :
( ! [B_y] : hAPP(c_Com_Obody,V_a_2) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y)
| hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(V_a_2))) )
& ! [V_a_2] :
( hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK4_skl(V_a_2))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(V_a_2))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(B_y,sK4_skl(V_a_2))],[f5333]) ).
fof(f5335,plain,
! [X0] :
( hAPP(c_Com_Obody,X0) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK4_skl(X0))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X0))) ),
inference(cnf_transformation,[status(thm)],[f5334]) ).
fof(f5336,plain,
! [X0,X1] :
( hAPP(c_Com_Obody,X0) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1)
| hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X0))) ),
inference(cnf_transformation,[status(thm)],[f5334]) ).
fof(f5351,plain,
! [V_m_2,T_b,V_a_2,T_a] :
( ? [B_b] : hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),B_b)
| ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2))) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f5352,plain,
! [V_m_2,T_b,V_a_2] :
( ? [B_b] : hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),B_b)
| ! [T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2))) ),
inference(miniscoping,[status(thm)],[f5351]) ).
fof(f5353,plain,
! [V_m_2,T_b,V_a_2] :
( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),sK5_skl(V_a_2,T_b,V_m_2))
| ! [T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(B_b,sK5_skl(V_a_2,T_b,V_m_2))],[f5352]) ).
fof(f5354,plain,
! [X0,X1,X2,X3] :
( hAPP(X3,X1) = hAPP(c_Option_Ooption_OSome(X2),sK5_skl(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X1),c_Map_Odom(X0,X2,X3))) ),
inference(cnf_transformation,[status(thm)],[f5353]) ).
fof(f5380,plain,
! [V_pn] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(V_pn)))
| hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f5381,plain,
! [X0] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X0)))
| hAPP(c_Com_Obody,X0) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
inference(cnf_transformation,[status(thm)],[f5380]) ).
fof(f19978,plain,
c_Com_OWT__bodies,
inference(cnf_transformation,[status(thm)],[f5246]) ).
fof(f19980,plain,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))),
inference(cnf_transformation,[status(thm)],[f5248]) ).
fof(f19981,plain,
~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn)))),
inference(cnf_transformation,[status(thm)],[f5250]) ).
fof(f20378,plain,
hBOOL(hAPP(c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody),v_pn)),
inference(resolution,[status(thm)],[f5262,f19980]) ).
fof(f20384,plain,
! [X0] : hBOOL(hAPP(hAPP(c_member(X0),v_pn),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))),
inference(resolution,[status(thm)],[f20378,f5263]) ).
fof(f20402,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Com_OWT,X1))
| hAPP(c_Com_Obody,X0) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f5283,f19978]) ).
fof(f22079,plain,
! [X0] :
( hAPP(c_Com_Obody,X0) = c_Option_Ooption_ONone(tc_Com_Ocom)
| hAPP(c_Com_Obody,X0) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK4_skl(X0)) ),
inference(resolution,[status(thm)],[f5335,f5381]) ).
fof(f22080,plain,
! [X0] :
( hBOOL(hAPP(c_Com_OWT,sK4_skl(X0)))
| hAPP(c_Com_Obody,X0) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
inference(resolution,[status(thm)],[f22079,f20402]) ).
fof(f22086,plain,
! [X0] :
( hAPP(c_Com_Obody,X0) = c_Option_Ooption_ONone(tc_Com_Ocom)
| hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X0)) = sK4_skl(X0) ),
inference(paramodulation,[status(thm)],[f22079,f5331]) ).
fof(f22156,plain,
( hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_ONone(tc_Com_Ocom)
| ~ hBOOL(hAPP(c_Com_OWT,sK4_skl(v_pn))) ),
inference(paramodulation,[status(thm)],[f22086,f19981]) ).
fof(f22170,plain,
hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_ONone(tc_Com_Ocom),
inference(forward_subsumption_resolution,[status(thm)],[f22156,f22080]) ).
fof(f22171,plain,
~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Option_Othe(tc_Com_Ocom),c_Option_Ooption_ONone(tc_Com_Ocom)))),
inference(backward_demodulation,[status(thm)],[f22170,f19981]) ).
fof(f22311,plain,
hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK5_skl(v_pn,tc_Com_Ocom,c_Com_Obody)),
inference(resolution,[status(thm)],[f5354,f20384]) ).
fof(f22312,plain,
c_Option_Ooption_ONone(tc_Com_Ocom) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK5_skl(v_pn,tc_Com_Ocom,c_Com_Obody)),
inference(forward_demodulation,[status(thm)],[f22170,f22311]) ).
fof(f22315,plain,
! [X0] :
( hAPP(c_Com_Obody,X0) != c_Option_Ooption_ONone(tc_Com_Ocom)
| hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X0))) ),
inference(paramodulation,[status(thm)],[f22312,f5336]) ).
fof(f22333,plain,
! [X0] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OBODY(X0))),
inference(forward_subsumption_resolution,[status(thm)],[f22315,f5381]) ).
fof(f22334,plain,
! [X0] : hAPP(c_Com_Obody,X0) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK4_skl(X0)),
inference(backward_subsumption_resolution,[status(thm)],[f5335,f22333]) ).
fof(f22341,plain,
! [X0] : hBOOL(hAPP(c_Com_OWT,sK4_skl(X0))),
inference(resolution,[status(thm)],[f22334,f20402]) ).
fof(f22349,plain,
! [X0] : hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X0)) = sK4_skl(X0),
inference(paramodulation,[status(thm)],[f22334,f5331]) ).
fof(f22534,plain,
hAPP(c_Option_Othe(tc_Com_Ocom),c_Option_Ooption_ONone(tc_Com_Ocom)) = sK4_skl(v_pn),
inference(paramodulation,[status(thm)],[f22170,f22349]) ).
fof(f22570,plain,
~ hBOOL(hAPP(c_Com_OWT,sK4_skl(v_pn))),
inference(backward_demodulation,[status(thm)],[f22534,f22171]) ).
fof(f22584,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f22570,f22341]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW374+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n012.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 09:49:43 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.13/5.95 % Drodi V4.1.1
% 1.75/6.25 % Refutation found
% 1.75/6.25 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.75/6.25 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.98/6.38 % Elapsed time: 0.997277 seconds
% 1.98/6.38 % CPU time: 3.023935 seconds
% 1.98/6.38 % Total memory used: 673.636 MB
% 1.98/6.38 % Net memory used: 667.319 MB
%------------------------------------------------------------------------------