%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW379+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 : n004.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 03:07:45 PM UTC 2026
% Result : Theorem 130.71s 18.06s
% Output : CNFRefutation 116.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 20 unt; 0 def)
% Number of atoms : 42 ( 33 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 13 ~; 10 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 86 ( 85 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [V_g_2,V_f_2] :
( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
=> V_f_2 = V_g_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1876,axiom,
! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),V_P_2) = V_P_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3530,axiom,
! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3537,axiom,
c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3867,axiom,
! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5222,axiom,
! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(hAPP(hAPP(c_COMBS(T_b,T_c,T_a),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5223,axiom,
! [V_y_2,V_x_2] :
( V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5224,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
| V_x_2 != V_y_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5242,plain,
! [V_g_2,V_f_2] :
( V_f_2 = V_g_2
| ? [B_x] : hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f5243,plain,
! [V_g_2,V_f_2] :
( V_f_2 = V_g_2
| hAPP(V_f_2,sK0_skl(V_f_2,V_g_2)) != hAPP(V_g_2,sK0_skl(V_f_2,V_g_2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B_x,sK0_skl(V_f_2,V_g_2))],[f5242]) ).
fof(f5244,plain,
! [X0,X1] :
( X0 = X1
| hAPP(X0,sK0_skl(X0,X1)) != hAPP(X1,sK0_skl(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f5243]) ).
fof(f10970,plain,
! [X0,X1] : X0 = hAPP(c_Set_OCollect(X1),X0),
inference(cnf_transformation,[status(thm)],[f1876]) ).
fof(f15854,plain,
! [X0,X1] : X0 = hAPP(c_Fun_Oid(X1),X0),
inference(cnf_transformation,[status(thm)],[f3530]) ).
fof(f15867,plain,
c_Fun_Oid(tc_Int_Oint) = c_Int_Oring__1__class_Oof__int(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f3537]) ).
fof(f16733,plain,
! [X0,X1,X2] : X0 != hAPP(hAPP(c_List_Olist_OCons(X1),X2),X0),
inference(cnf_transformation,[status(thm)],[f3867]) ).
fof(f19955,plain,
! [X0,X1,X2,X3,X4,X5] : hAPP(hAPP(X0,X1),hAPP(X2,X1)) = hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),X0),X2),X1),
inference(cnf_transformation,[status(thm)],[f5222]) ).
fof(f19956,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal,X0),X1)) ),
inference(cnf_transformation,[status(thm)],[f5223]) ).
fof(f19957,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fequal,X0),X1))
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f5224]) ).
fof(f20363,plain,
! [X0] : hBOOL(hAPP(hAPP(c_fequal,X0),X0)),
inference(destructive_equality_resolution,[status(thm)],[f19957]) ).
fof(f21128,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(X3,X4) = X4
| ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X0,X1,X2),c_fequal),X3),X4)) ),
inference(paramodulation,[status(thm)],[f19955,f19956]) ).
fof(f23623,plain,
! [X0,X1,X2,X3,X4,X5] : hAPP(hAPP(X0,X1),X1) = hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),X0),c_Fun_Oid(X5)),X1),
inference(paramodulation,[status(thm)],[f15854,f19955]) ).
fof(f24239,plain,
! [X0,X1,X2,X3,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X0,X1,X2),X3),c_Set_OCollect(X4)),X5) = hAPP(hAPP(X3,X5),X5),
inference(paramodulation,[status(thm)],[f10970,f19955]) ).
fof(f26023,plain,
! [X0,X1,X2,X3,X4] : hBOOL(hAPP(hAPP(hAPP(c_COMBS(X0,X1,X2),c_fequal),c_Fun_Oid(X3)),X4)),
inference(paramodulation,[status(thm)],[f23623,f20363]) ).
fof(f26279,plain,
! [X0,X1,X2,X3] : hBOOL(hAPP(hAPP(hAPP(c_COMBS(X0,X1,X2),c_fequal),c_Int_Oring__1__class_Oof__int(tc_Int_Oint)),X3)),
inference(paramodulation,[status(thm)],[f15867,f26023]) ).
fof(f26281,plain,
! [X0] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0) = X0,
inference(resolution,[status(thm)],[f26279,f21128]) ).
fof(f26326,plain,
! [X0] :
( c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = X0
| sK0_skl(X0,c_Int_Oring__1__class_Oof__int(tc_Int_Oint)) != hAPP(X0,sK0_skl(X0,c_Int_Oring__1__class_Oof__int(tc_Int_Oint))) ),
inference(paramodulation,[status(thm)],[f26281,f5244]) ).
fof(f27015,plain,
! [X0] :
( c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Set_OCollect(X0)
| sK0_skl(c_Set_OCollect(X0),c_Int_Oring__1__class_Oof__int(tc_Int_Oint)) != sK0_skl(c_Set_OCollect(X0),c_Int_Oring__1__class_Oof__int(tc_Int_Oint)) ),
inference(paramodulation,[status(thm)],[f10970,f26326]) ).
fof(f27048,plain,
! [X0] : c_Set_OCollect(X0) = c_Int_Oring__1__class_Oof__int(tc_Int_Oint),
inference(trivial_equality_resolution,[status(thm)],[f27015]) ).
fof(f28065,plain,
! [X0,X1,X2,X3,X4] : hAPP(hAPP(hAPP(c_COMBS(X0,X1,X2),X3),c_Int_Oring__1__class_Oof__int(tc_Int_Oint)),X4) = hAPP(hAPP(X3,X4),X4),
inference(forward_demodulation,[status(thm)],[f27048,f24239]) ).
fof(f29532,plain,
! [X0,X1,X2,X3,X4,X5] : hAPP(X0,X1) != hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_List_Olist_OCons(X5)),X0),X1),
inference(paramodulation,[status(thm)],[f19955,f16733]) ).
fof(f29544,plain,
$false,
inference(resolution,[status(thm)],[f29532,f28065]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW379+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n004.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Mon Sep 21 09:49:50 UTC 2026
% 0.19/0.47 % CPUTime :
% 1.25/1.56 % Drodi V4.1.1
% 130.71/18.06 % Refutation found
% 130.71/18.06 % SZS status Theorem for theBenchmark: Theorem is valid
% 130.71/18.06 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 23.50/18.35 % Elapsed time: 17.860388 seconds
% 23.50/18.35 % CPU time: 132.099102 seconds
% 23.50/18.35 % Total memory used: 1.314 GB
% 23.50/18.35 % Net memory used: 1.292 GB
%------------------------------------------------------------------------------