TSTP Solution File: SWW368+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWW368+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:44:49 EDT 2023
% Result : Theorem 3.61s 1.22s
% Output : CNFRefutation 3.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 34 ( 16 unt; 0 def)
% Number of atoms : 64 ( 9 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 52 ( 22 ~; 18 |; 6 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 61 (; 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [V_b_2,V_B_2,V_a_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
=> V_a_2 = V_b_2 )
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [V_B_2,V_a_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [V_B_2,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2))
<=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5225,hypothesis,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5228,hypothesis,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5230,conjecture,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),v_G)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5231,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),v_G)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
inference(negated_conjecture,[status(cth)],[f5230]) ).
fof(f5258,plain,
! [V_b_2,V_B_2,V_a_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
& V_a_2 != V_b_2 )
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f5260,plain,
! [X0,X1,X2,X3] :
( X0 != X1
| hBOOL(hAPP(hAPP(c_member(X2),X0),hAPP(hAPP(c_Set_Oinsert(X2),X1),X3))) ),
inference(cnf_transformation,[status(esa)],[f5258]) ).
fof(f5328,plain,
! [V_A_2,V_a_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ),
inference(pre_NNF_transformation,[status(esa)],[f32]) ).
fof(f5329,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_member(X0),X1),X2))
| hAPP(hAPP(c_Set_Oinsert(X0),X1),X2) = X2 ),
inference(cnf_transformation,[status(esa)],[f5328]) ).
fof(f5381,plain,
! [X0,X1,X2,X3,X4] : hAPP(c_Set_Oimage(X0,X1,X2),hAPP(hAPP(c_Set_Oinsert(X0),X3),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X0,X1,X2),X4)),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f5396,plain,
! [V_B_2,V_A_2,V_x_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2))
| ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
inference(NNF_transformation,[status(esa)],[f53]) ).
fof(f5397,plain,
( ! [V_B_2,V_A_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2))
| ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) )
& ! [V_B_2,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
inference(miniscoping,[status(esa)],[f5396]) ).
fof(f5400,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X2),X3)) ),
inference(cnf_transformation,[status(esa)],[f5397]) ).
fof(f20146,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
inference(cnf_transformation,[status(esa)],[f5225]) ).
fof(f20149,plain,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_U)),
inference(cnf_transformation,[status(esa)],[f5228]) ).
fof(f20151,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),v_G)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
inference(cnf_transformation,[status(esa)],[f5231]) ).
fof(f20431,plain,
! [X0,X1,X2] : hBOOL(hAPP(hAPP(c_member(X0),X1),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2))),
inference(destructive_equality_resolution,[status(esa)],[f5260]) ).
fof(f20933,plain,
hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),v_pn),v_U) = v_U,
inference(resolution,[status(thm)],[f5329,f20149]) ).
fof(f21962,plain,
! [X0,X1,X2,X3,X4] : hBOOL(hAPP(hAPP(c_member(X0),hAPP(X1,X2)),hAPP(c_Set_Oimage(X3,X0,X1),hAPP(hAPP(c_Set_Oinsert(X3),X2),X4)))),
inference(paramodulation,[status(thm)],[f5381,f20431]) ).
fof(f22553,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X0),hAPP(X1,v_pn)),hAPP(c_Set_Oimage(tc_Com_Opname,X0,X1),v_U))),
inference(paramodulation,[status(thm)],[f20933,f21962]) ).
fof(f24417,plain,
( spl0_30
<=> hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,v_pn)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ),
introduced(split_symbol_definition) ).
fof(f24419,plain,
( ~ hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,v_pn)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| spl0_30 ),
inference(component_clause,[status(thm)],[f24417]) ).
fof(f24420,plain,
( spl0_31
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ),
introduced(split_symbol_definition) ).
fof(f24422,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| spl0_31 ),
inference(component_clause,[status(thm)],[f24420]) ).
fof(f24423,plain,
( ~ hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,v_pn)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ),
inference(resolution,[status(thm)],[f5400,f20151]) ).
fof(f24424,plain,
( ~ spl0_30
| ~ spl0_31 ),
inference(split_clause,[status(thm)],[f24423,f24417,f24420]) ).
fof(f24438,plain,
( $false
| spl0_30 ),
inference(forward_subsumption_resolution,[status(thm)],[f24419,f22553]) ).
fof(f24439,plain,
spl0_30,
inference(contradiction_clause,[status(thm)],[f24438]) ).
fof(f24440,plain,
( $false
| spl0_31 ),
inference(forward_subsumption_resolution,[status(thm)],[f24422,f20146]) ).
fof(f24441,plain,
spl0_31,
inference(contradiction_clause,[status(thm)],[f24440]) ).
fof(f24442,plain,
$false,
inference(sat_refutation,[status(thm)],[f24424,f24439,f24441]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW368+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue May 30 11:01:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.61/0.78 % Drodi V3.5.1
% 3.61/1.22 % Refutation found
% 3.61/1.22 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.61/1.22 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.89/1.31 % Elapsed time: 0.951821 seconds
% 3.89/1.31 % CPU time: 4.032932 seconds
% 3.89/1.31 % Memory used: 617.191 MB
%------------------------------------------------------------------------------