%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW396+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 03:07:47 PM UTC 2026
% Result : Theorem 16.08s 3.04s
% Output : CNFRefutation 16.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 27 unt; 0 def)
% Number of atoms : 47 ( 38 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 9 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 89 ( 88 !; 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/sandbox/benchmark/theBenchmark.p') ).
fof(f752,axiom,
! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2049,axiom,
! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2236,axiom,
c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2854,axiom,
! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3983,axiom,
! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5207,axiom,
! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Qa_2,V_R_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5208,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/sandbox/benchmark/theBenchmark.p') ).
fof(f5209,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/sandbox/benchmark/theBenchmark.p') ).
fof(f5227,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(f5228,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))],[f5227]) ).
fof(f5229,plain,
! [X0,X1] :
( X0 = X1
| hAPP(X0,sK0_skl(X0,X1)) != hAPP(X1,sK0_skl(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f5228]) ).
fof(f7413,plain,
! [X0,X1] : hAPP(c_Fun_Oid(X0),X1) = X1,
inference(cnf_transformation,[status(thm)],[f752]) ).
fof(f11304,plain,
! [X0] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X0) = X0,
inference(cnf_transformation,[status(thm)],[f2049]) ).
fof(f11792,plain,
c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f2236]) ).
fof(f13626,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0,
inference(cnf_transformation,[status(thm)],[f2854]) ).
fof(f17078,plain,
! [X0,X1,X2] : hAPP(hAPP(c_List_Olist_OCons(X0),X1),X2) != X2,
inference(cnf_transformation,[status(thm)],[f3983]) ).
fof(f19982,plain,
! [X0,X1,X2,X3,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X0,X1,X2),X3),X4),X5) = hAPP(hAPP(X3,X5),hAPP(X4,X5)),
inference(cnf_transformation,[status(thm)],[f5207]) ).
fof(f19983,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal,X0),X1)) ),
inference(cnf_transformation,[status(thm)],[f5208]) ).
fof(f19984,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fequal,X0),X1))
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f5209]) ).
fof(f20843,plain,
! [X0] : hBOOL(hAPP(hAPP(c_fequal,X0),X0)),
inference(destructive_equality_resolution,[status(thm)],[f19984]) ).
fof(f21395,plain,
! [X0,X1,X2,X3,X4] :
( X4 = hAPP(X3,X4)
| ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X0,X1,X2),c_fequal),X3),X4)) ),
inference(paramodulation,[status(thm)],[f19982,f19983]) ).
fof(f23300,plain,
! [X0,X1,X2,X3,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X0,X1,X2),X3),c_Fun_Oid(X4)),X5) = hAPP(hAPP(X3,X5),X5),
inference(paramodulation,[status(thm)],[f7413,f19982]) ).
fof(f25991,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)],[f23300,f20843]) ).
fof(f26233,plain,
! [X0,X1,X2,X3,X4] : hAPP(hAPP(hAPP(c_COMBS(X0,X1,X2),c_Nat_Osize__class_Osize(tc_Nat_Onat)),c_Fun_Oid(X3)),X4) = hAPP(X4,X4),
inference(paramodulation,[status(thm)],[f11304,f23300]) ).
fof(f26271,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)],[f11792,f25991]) ).
fof(f26799,plain,
! [X0] : X0 = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0),
inference(resolution,[status(thm)],[f26271,f21395]) ).
fof(f26815,plain,
! [X0] :
( 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))) != sK0_skl(X0,c_Int_Oring__1__class_Oof__int(tc_Int_Oint)) ),
inference(paramodulation,[status(thm)],[f26799,f5229]) ).
fof(f27732,plain,
c_Int_Onumber__class_Onumber__of(tc_Int_Oint) = c_Int_Oring__1__class_Oof__int(tc_Int_Oint),
inference(resolution,[status(thm)],[f26815,f13626]) ).
fof(f27734,plain,
! [X0] : c_Fun_Oid(X0) = c_Int_Oring__1__class_Oof__int(tc_Int_Oint),
inference(resolution,[status(thm)],[f26815,f7413]) ).
fof(f27736,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat) = c_Int_Oring__1__class_Oof__int(tc_Int_Oint),
inference(resolution,[status(thm)],[f26815,f11304]) ).
fof(f27891,plain,
! [X0] : c_Fun_Oid(X0) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint),
inference(backward_demodulation,[status(thm)],[f27732,f27734]) ).
fof(f27903,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint),
inference(forward_demodulation,[status(thm)],[f27732,f27736]) ).
fof(f29684,plain,
! [X0,X1,X2,X3,X4] : hAPP(hAPP(hAPP(c_COMBS(X0,X1,X2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint)),c_Fun_Oid(X3)),X4) = hAPP(X4,X4),
inference(forward_demodulation,[status(thm)],[f27903,f26233]) ).
fof(f29685,plain,
! [X0,X1,X2,X3] : hAPP(hAPP(hAPP(c_COMBS(X0,X1,X2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint)),X3) = hAPP(X3,X3),
inference(forward_demodulation,[status(thm)],[f27891,f29684]) ).
fof(f30383,plain,
! [X0,X1,X2,X3,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X0,X1,X2),c_List_Olist_OCons(X3)),X4),X5) != hAPP(X4,X5),
inference(paramodulation,[status(thm)],[f19982,f17078]) ).
fof(f30431,plain,
$false,
inference(resolution,[status(thm)],[f30383,f29685]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW396+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 09:56:29 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.81/1.05 % Drodi V4.1.1
% 16.08/3.04 % Refutation found
% 16.08/3.04 % SZS status Theorem for theBenchmark: Theorem is valid
% 16.08/3.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 16.08/3.17 % Elapsed time: 2.801004 seconds
% 16.08/3.17 % CPU time: 16.888240 seconds
% 16.08/3.17 % Total memory used: 897.089 MB
% 16.08/3.17 % Net memory used: 888.687 MB
%------------------------------------------------------------------------------