TSTP Solution File: LCL776-1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : LCL776-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n015.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 12:20:27 EDT 2023
% Result : Unsatisfiable 2.20s 0.83s
% Output : CNFRefutation 2.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 47 ( 23 unt; 0 def)
% Number of atoms : 74 ( 37 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 56 ( 29 ~; 25 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-5 aty)
% Number of variables : 99 (; 99 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f724,axiom,
! [V_xs,V_x,V_ts,T_a] : c_List_Oappend(V_xs,c_List_Oappend(V_x,V_ts,T_a),T_a) = c_List_Oappend(c_List_Oappend(V_xs,V_x,T_a),V_ts,T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f728,axiom,
! [V_x,V_s,V_t] :
( c_List_Oappend(V_x,c_List_Olist_OCons(V_s,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) = c_List_Olist_ONil(tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_x,tc_Lambda_OdB,tc_Lambda_OdB)),V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Oappend(V_x,c_List_Olist_OCons(V_s,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f745,axiom,
! [V_ys,V_xs,T_a] :
( V_ys != c_List_Oappend(V_xs,V_ys,T_a)
| V_xs = c_List_Olist_ONil(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f751,axiom,
! [T_a,V_a_H,V_list_H] : c_List_Olist_ONil(T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f760,axiom,
! [V_xs,V_ys,T_a] :
( c_List_Oappend(V_xs,V_ys,T_a) != c_List_Olist_ONil(T_a)
| V_ys = c_List_Olist_ONil(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f768,axiom,
! [V_r,V_s,V_ss] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r)),V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,V_s))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(V_r,V_s,c_HOL_Ozero__class_Ozero(tc_nat)),V_ss,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f773,axiom,
! [V_xs,T_a] : V_xs = c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f779,axiom,
! [V_f,V_a,V_x,V_xs,T_b,T_a] : c_List_Ofoldl(V_f,V_a,c_List_Olist_OCons(V_x,V_xs,T_b),T_a,T_b) = c_List_Ofoldl(V_f,hAPP(hAPP(V_f,V_a),V_x),V_xs,T_a,T_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f782,axiom,
! [V_x,V_xa,T_a,V_zs] : c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f801,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f802,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,v_s)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f804,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r)),v_s),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1955,plain,
! [X0,X1,X2,X3] : c_List_Oappend(X0,c_List_Oappend(X1,X2,X3),X3) = c_List_Oappend(c_List_Oappend(X0,X1,X3),X2,X3),
inference(cnf_transformation,[status(esa)],[f724]) ).
fof(f1959,plain,
! [V_x,V_s] :
( c_List_Oappend(V_x,c_List_Olist_OCons(V_s,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) = c_List_Olist_ONil(tc_Lambda_OdB)
| ! [V_t] : hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_x,tc_Lambda_OdB,tc_Lambda_OdB)),V_s) = c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Oappend(V_x,c_List_Olist_OCons(V_s,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(miniscoping,[status(esa)],[f728]) ).
fof(f1960,plain,
! [X0,X1,X2] :
( c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) = c_List_Olist_ONil(tc_Lambda_OdB)
| hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X0,tc_Lambda_OdB,tc_Lambda_OdB)),X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,X2,c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(cnf_transformation,[status(esa)],[f1959]) ).
fof(f1983,plain,
! [V_xs,T_a] :
( ! [V_ys] : V_ys != c_List_Oappend(V_xs,V_ys,T_a)
| V_xs = c_List_Olist_ONil(T_a) ),
inference(miniscoping,[status(esa)],[f745]) ).
fof(f1984,plain,
! [X0,X1,X2] :
( X0 != c_List_Oappend(X1,X0,X2)
| X1 = c_List_Olist_ONil(X2) ),
inference(cnf_transformation,[status(esa)],[f1983]) ).
fof(f1994,plain,
! [X0,X1,X2] : c_List_Olist_ONil(X0) != c_List_Olist_OCons(X1,X2,X0),
inference(cnf_transformation,[status(esa)],[f751]) ).
fof(f2010,plain,
! [V_ys,T_a] :
( ! [V_xs] : c_List_Oappend(V_xs,V_ys,T_a) != c_List_Olist_ONil(T_a)
| V_ys = c_List_Olist_ONil(T_a) ),
inference(miniscoping,[status(esa)],[f760]) ).
fof(f2011,plain,
! [X0,X1,X2] :
( c_List_Oappend(X0,X1,X2) != c_List_Olist_ONil(X2)
| X1 = c_List_Olist_ONil(X2) ),
inference(cnf_transformation,[status(esa)],[f2010]) ).
fof(f2022,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X0,X1,c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(cnf_transformation,[status(esa)],[f768]) ).
fof(f2027,plain,
! [X0,X1] : X0 = c_List_Oappend(X0,c_List_Olist_ONil(X1),X1),
inference(cnf_transformation,[status(esa)],[f773]) ).
fof(f2035,plain,
! [X0,X1,X2,X3,X4,X5] : c_List_Ofoldl(X0,X1,c_List_Olist_OCons(X2,X3,X4),X5,X4) = c_List_Ofoldl(X0,hAPP(hAPP(X0,X1),X2),X3,X5,X4),
inference(cnf_transformation,[status(esa)],[f779]) ).
fof(f2039,plain,
! [X0,X1,X2,X3] : c_List_Oappend(c_List_Olist_OCons(X0,X1,X2),X3,X2) = c_List_Olist_OCons(X0,c_List_Oappend(X1,X3,X2),X2),
inference(cnf_transformation,[status(esa)],[f782]) ).
fof(f2061,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
inference(cnf_transformation,[status(esa)],[f801]) ).
fof(f2062,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_s)),
inference(cnf_transformation,[status(esa)],[f802]) ).
fof(f2064,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r)),v_s),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(cnf_transformation,[status(esa)],[f804]) ).
fof(f2138,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r),c_List_Olist_OCons(v_s,c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(paramodulation,[status(thm)],[f2035,f2064]) ).
fof(f2164,plain,
! [X0,X1,X2,X3] :
( X0 = c_List_Olist_ONil(X1)
| X2 != c_List_Oappend(c_List_Oappend(X3,X0,X1),X2,X1) ),
inference(resolution,[status(thm)],[f2011,f1984]) ).
fof(f2226,plain,
! [X0,X1,X2,X3] :
( X0 = c_List_Olist_ONil(X1)
| X2 != c_List_Oappend(X3,c_List_Oappend(X0,X2,X1),X1) ),
inference(backward_demodulation,[status(thm)],[f1955,f2164]) ).
fof(f2329,plain,
! [X0,X1,X2,X3,X4] :
( c_List_Olist_OCons(X0,X1,X2) = c_List_Olist_ONil(X2)
| X3 != c_List_Oappend(X4,c_List_Olist_OCons(X0,c_List_Oappend(X1,X3,X2),X2),X2) ),
inference(paramodulation,[status(thm)],[f2039,f2226]) ).
fof(f2330,plain,
! [X0,X1,X2,X3,X4] : X0 != c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Oappend(X3,X0,X4),X4),X4),
inference(forward_subsumption_resolution,[status(thm)],[f2329,f1994]) ).
fof(f2393,plain,
! [X0,X1,X2,X3] : c_List_Olist_ONil(X0) != c_List_Oappend(X1,c_List_Olist_OCons(X2,X3,X0),X0),
inference(paramodulation,[status(thm)],[f2027,f2330]) ).
fof(f2416,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2) = c_List_Ofoldl(c_Lambda_OdB_OApp,X0,c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
inference(forward_subsumption_resolution,[status(thm)],[f1960,f2393]) ).
fof(f3195,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0),c_List_Olist_OCons(X1,X2,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X0,X1,c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(forward_demodulation,[status(thm)],[f2035,f2022]) ).
fof(f3196,plain,
( spl0_7
<=> hBOOL(hAPP(c_InductTermi_OIT,v_s)) ),
introduced(split_symbol_definition) ).
fof(f3198,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,v_s))
| spl0_7 ),
inference(component_clause,[status(thm)],[f3196]) ).
fof(f3199,plain,
( spl0_8
<=> hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ),
introduced(split_symbol_definition) ).
fof(f3201,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
| spl0_8 ),
inference(component_clause,[status(thm)],[f3199]) ).
fof(f3202,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,v_s))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(resolution,[status(thm)],[f3195,f2138]) ).
fof(f3203,plain,
( ~ spl0_7
| ~ spl0_8 ),
inference(split_clause,[status(thm)],[f3202,f3196,f3199]) ).
fof(f3206,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f3198,f2062]) ).
fof(f3207,plain,
spl0_7,
inference(contradiction_clause,[status(thm)],[f3206]) ).
fof(f3208,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i))))
| spl0_8 ),
inference(forward_demodulation,[status(thm)],[f2416,f3201]) ).
fof(f3209,plain,
( $false
| spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f3208,f2061]) ).
fof(f3210,plain,
spl0_8,
inference(contradiction_clause,[status(thm)],[f3209]) ).
fof(f3211,plain,
$false,
inference(sat_refutation,[status(thm)],[f3203,f3207,f3210]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LCL776-1 : TPTP v8.1.2. Released v4.1.0.
% 0.10/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n015.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue May 30 09:58:34 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.36 % Drodi V3.5.1
% 2.20/0.83 % Refutation found
% 2.20/0.83 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.20/0.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.90/0.87 % Elapsed time: 0.550132 seconds
% 2.90/0.87 % CPU time: 2.950909 seconds
% 2.90/0.87 % Memory used: 134.187 MB
%------------------------------------------------------------------------------