%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC419-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 02:41:10 PM UTC 2026
% Result : Unsatisfiable 19.86s 2.94s
% Output : CNFRefutation 19.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 27
% Syntax : Number of formulae : 85 ( 22 unt; 12 def)
% Number of atoms : 182 ( 37 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 189 ( 92 ~; 85 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 13 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f73,axiom,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f74,axiom,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [U,V] :
( ssList(cons(U,V))
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f188,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f190,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
! [A,B,C] :
( app(app(C,cons(A,nil)),B) != sk1
| app(app(B,cons(A,nil)),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f201,plain,
strictorderedP(nil),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f206,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f209,plain,
~ singletonP(nil),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f272,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f273,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f285,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f431,plain,
ssList(sk3),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f433,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f434,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f435,plain,
neq(sk2,nil),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f436,plain,
! [X0,X1,X2] :
( app(app(X2,cons(X0,nil)),X1) != sk1
| app(app(X1,cons(X0,nil)),X2) != sk2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f438,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f439,plain,
( ~ neq(sk4,nil)
| ssList(sk6) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f440,plain,
( ~ neq(sk4,nil)
| app(cons(sk5,nil),sk6) = sk4 ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f441,plain,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk3 ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f456,definition,
( sQ4_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( ~ sQ4_spl
| ssItem(sk5) ),
inference(component_clause,[status(thm)],[f456]) ).
fof(f459,definition,
( sQ5_spl
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f461,plain,
( sQ5_spl
| ~ neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f459]) ).
fof(f462,plain,
( ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f438,f456,f459]) ).
fof(f463,definition,
( sQ6_spl
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f466,plain,
( ~ sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f439,f463,f459]) ).
fof(f467,definition,
( sQ7_spl
<=> app(cons(sk5,nil),sk6) = sk4 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f468,plain,
( ~ sQ7_spl
| app(cons(sk5,nil),sk6) = sk4 ),
inference(component_clause,[status(thm)],[f467]) ).
fof(f470,plain,
( ~ sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f440,f467,f459]) ).
fof(f471,definition,
( sQ8_spl
<=> app(sk6,cons(sk5,nil)) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f472,plain,
( ~ sQ8_spl
| app(sk6,cons(sk5,nil)) = sk3 ),
inference(component_clause,[status(thm)],[f471]) ).
fof(f474,plain,
( ~ sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f441,f471,f459]) ).
fof(f513,definition,
( sQ9_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f515,plain,
( sQ9_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f513]) ).
fof(f530,plain,
app(sk3,nil) = sk3,
inference(resolution,[status(thm)],[f431,f272]) ).
fof(f537,definition,
( sQ12_spl
<=> ssList(sk3) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f539,plain,
( sQ12_spl
| ~ ssList(sk3) ),
inference(component_clause,[status(thm)],[f537]) ).
fof(f567,plain,
neq(sk4,nil),
inference(backward_demodulation,[status(thm)],[f433,f435]) ).
fof(f616,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f515,f206]) ).
fof(f617,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f616]) ).
fof(f661,plain,
! [X0,X1,X2] :
( app(app(X2,cons(X0,nil)),X1) != sk1
| app(app(X1,cons(X0,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f433,f436]) ).
fof(f662,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f461,f567]) ).
fof(f663,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f662]) ).
fof(f760,definition,
( sQ21_spl
<=> ssList(cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f761,plain,
( ~ sQ21_spl
| ssList(cons(sk5,nil)) ),
inference(component_clause,[status(thm)],[f760]) ).
fof(f762,plain,
( sQ21_spl
| ~ ssList(cons(sk5,nil)) ),
inference(component_clause,[status(thm)],[f760]) ).
fof(f847,plain,
! [X0] :
( ~ sQ4_spl
| ssList(cons(sk5,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f457,f285]) ).
fof(f898,plain,
! [X0] :
( ~ sQ8_spl
| app(sk3,X0) != sk1
| app(app(X0,cons(sk5,nil)),sk6) != sk4
| ~ ssList(sk6)
| ~ ssList(X0)
| ~ ssItem(sk5) ),
inference(paramodulation,[status(thm)],[f472,f661]) ).
fof(f900,definition,
! [X0] :
( sQ27_spl
<=> ( app(sk3,X0) != sk1
| app(app(X0,cons(sk5,nil)),sk6) != sk4
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f901,plain,
! [X0] :
( ~ sQ27_spl
| app(sk3,X0) != sk1
| app(app(X0,cons(sk5,nil)),sk6) != sk4
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f900]) ).
fof(f903,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| sQ27_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f898,f456,f900,f463,f471]) ).
fof(f1790,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f539,f431]) ).
fof(f1791,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f1790]) ).
fof(f2824,plain,
( ~ sQ4_spl
| sQ21_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f762,f847]) ).
fof(f2825,plain,
( ~ sQ4_spl
| sQ21_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f2824,f513,f760,f456]) ).
fof(f2931,definition,
( sQ102_spl
<=> strictorderedP(nil) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f2933,plain,
( sQ102_spl
| ~ strictorderedP(nil) ),
inference(component_clause,[status(thm)],[f2931]) ).
fof(f4734,plain,
( ~ sQ21_spl
| app(nil,cons(sk5,nil)) = cons(sk5,nil) ),
inference(resolution,[status(thm)],[f761,f273]) ).
fof(f5183,definition,
( sQ221_spl
<=> singletonP(nil) ),
introduced(definition,[new_symbols(definition,[sQ221_spl])],[split_symbol_definition]) ).
fof(f5184,plain,
( ~ sQ221_spl
| singletonP(nil) ),
inference(component_clause,[status(thm)],[f5183]) ).
fof(f5195,plain,
( ~ sQ221_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5184,f209]) ).
fof(f5196,plain,
~ sQ221_spl,
inference(contradiction_clause,[status(thm)],[f5195]) ).
fof(f5391,plain,
( sQ102_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2933,f201]) ).
fof(f5392,plain,
sQ102_spl,
inference(contradiction_clause,[status(thm)],[f5391]) ).
fof(f7688,plain,
! [X0] :
( ~ sQ27_spl
| app(sk3,X0) != sk3
| app(app(X0,cons(sk5,nil)),sk6) != sk4
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f434,f901]) ).
fof(f7689,plain,
( ~ sQ27_spl
| app(app(nil,cons(sk5,nil)),sk6) != sk4
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f7688,f530]) ).
fof(f7691,definition,
( sQ378_spl
<=> app(app(nil,cons(sk5,nil)),sk6) = sk4 ),
introduced(definition,[new_symbols(definition,[sQ378_spl])],[split_symbol_definition]) ).
fof(f7693,plain,
( sQ378_spl
| app(app(nil,cons(sk5,nil)),sk6) != sk4 ),
inference(component_clause,[status(thm)],[f7691]) ).
fof(f7694,plain,
( ~ sQ27_spl
| ~ sQ378_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f7689,f513,f7691,f900]) ).
fof(f7699,plain,
( sQ378_spl
| ~ sQ21_spl
| app(cons(sk5,nil),sk6) != sk4 ),
inference(forward_demodulation,[status(thm)],[f4734,f7693]) ).
fof(f7700,plain,
( sQ378_spl
| ~ sQ21_spl
| ~ sQ7_spl
| sk4 != sk4 ),
inference(forward_demodulation,[status(thm)],[f468,f7699]) ).
fof(f7701,plain,
( sQ378_spl
| ~ sQ21_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f7700]) ).
fof(f7702,plain,
( sQ378_spl
| ~ sQ21_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f7701]) ).
fof(f7703,plain,
$false,
inference(sat_refutation,[status(thm)],[f462,f466,f470,f474,f617,f663,f903,f1791,f2825,f5196,f5392,f7694,f7702]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC419-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n008.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 08:23:53 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 19.86/2.94 % Refutation found
% 19.86/2.94 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 19.86/2.94 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 19.86/2.98 % Elapsed time: 2.610798 seconds
% 19.86/2.98 % CPU time: 20.359421 seconds
% 19.86/2.98 % Total memory used: 296.439 MB
% 19.86/2.98 % Net memory used: 280.262 MB
%------------------------------------------------------------------------------