%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC104-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 02:39:58 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 22
% Syntax : Number of formulae : 72 ( 22 unt; 8 def)
% Number of atoms : 154 ( 22 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 158 ( 76 ~; 74 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 29 ( 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [U,V] :
( ssList(app(V,U))
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f100,axiom,
! [U,V] :
( V = U
| neq(V,U)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f115,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f144,axiom,
! [U,V,W] :
( frontsegP(W,U)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f188,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f189,negated_conjecture,
ssList(sk4),
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,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
app(sk3,sk5) = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( nil != sk3
| nil = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f206,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f284,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f301,plain,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f319,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ~ neq(U,V)
| U != V ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f320,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f319]) ).
fof(f358,plain,
! [U,W] :
( frontsegP(W,U)
| ~ ssList(W)
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| app(U,V) != W ) ),
inference(miniscoping,[status(thm)],[f144]) ).
fof(f359,plain,
! [X0,X1,X2] :
( frontsegP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != X2 ),
inference(cnf_transformation,[status(thm)],[f358]) ).
fof(f431,plain,
ssList(sk3),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f432,plain,
ssList(sk4),
inference(cnf_transformation,[status(thm)],[f189]) ).
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,
ssList(sk5),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f437,plain,
app(sk3,sk5) = sk4,
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f441,plain,
( nil != sk3
| nil = sk4 ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f442,plain,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f450,definition,
( sQ2_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f451,plain,
( ~ sQ2_spl
| nil = sk4 ),
inference(component_clause,[status(thm)],[f450]) ).
fof(f453,definition,
( sQ3_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f456,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f441,f450,f453]) ).
fof(f457,definition,
( sQ4_spl
<=> neq(sk1,nil) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f459,plain,
( sQ4_spl
| ~ neq(sk1,nil) ),
inference(component_clause,[status(thm)],[f457]) ).
fof(f460,definition,
( sQ5_spl
<=> frontsegP(sk2,sk1) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f462,plain,
( sQ5_spl
| ~ frontsegP(sk2,sk1) ),
inference(component_clause,[status(thm)],[f460]) ).
fof(f463,plain,
( ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f442,f457,f460]) ).
fof(f471,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f320]) ).
fof(f472,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f471]) ).
fof(f479,plain,
! [X0,X1] :
( frontsegP(app(X1,X0),X1)
| ~ ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f359]) ).
fof(f497,plain,
neq(sk4,nil),
inference(forward_demodulation,[status(thm)],[f433,f435]) ).
fof(f498,plain,
( ~ sQ2_spl
| neq(sk4,sk4) ),
inference(forward_demodulation,[status(thm)],[f451,f497]) ).
fof(f499,plain,
( sQ4_spl
| ~ neq(sk3,nil) ),
inference(forward_demodulation,[status(thm)],[f434,f459]) ).
fof(f512,plain,
( ~ sQ2_spl
| ~ ssList(sk4) ),
inference(resolution,[status(thm)],[f472,f498]) ).
fof(f513,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f512,f432]) ).
fof(f514,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f513]) ).
fof(f517,definition,
( sQ6_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f519,plain,
( sQ6_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f517]) ).
fof(f525,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f519,f206]) ).
fof(f526,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f525]) ).
fof(f528,definition,
( sQ8_spl
<=> ssList(sk5) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f530,plain,
( sQ8_spl
| ~ ssList(sk5) ),
inference(component_clause,[status(thm)],[f528]) ).
fof(f531,definition,
( sQ9_spl
<=> ssList(sk3) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f533,plain,
( sQ9_spl
| ~ ssList(sk3) ),
inference(component_clause,[status(thm)],[f531]) ).
fof(f538,plain,
( sQ4_spl
| sk3 = nil
| ~ ssList(sk3)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f301,f499]) ).
fof(f541,plain,
( sQ4_spl
| sQ3_spl
| ~ sQ9_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f538,f517,f531,f453,f457]) ).
fof(f542,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f533,f431]) ).
fof(f543,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f542]) ).
fof(f544,plain,
( sQ5_spl
| ~ frontsegP(sk4,sk1) ),
inference(forward_demodulation,[status(thm)],[f433,f462]) ).
fof(f545,plain,
( sQ5_spl
| ~ frontsegP(sk4,sk3) ),
inference(forward_demodulation,[status(thm)],[f434,f544]) ).
fof(f546,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f530,f436]) ).
fof(f547,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f546]) ).
fof(f582,plain,
! [X0,X1] :
( frontsegP(app(X1,X0),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f479,f284]) ).
fof(f584,plain,
( frontsegP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(sk5) ),
inference(paramodulation,[status(thm)],[f437,f582]) ).
fof(f587,definition,
( sQ15_spl
<=> frontsegP(sk4,sk3) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f588,plain,
( ~ sQ15_spl
| frontsegP(sk4,sk3) ),
inference(component_clause,[status(thm)],[f587]) ).
fof(f590,plain,
( sQ15_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f584,f528,f531,f587]) ).
fof(f591,plain,
( ~ sQ15_spl
| sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f588,f545]) ).
fof(f592,plain,
( ~ sQ15_spl
| sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f591]) ).
fof(f593,plain,
$false,
inference(sat_refutation,[status(thm)],[f456,f463,f514,f526,f541,f543,f547,f590,f592]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC104-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 07:58:14 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.081129 seconds
% 0.13/0.44 % CPU time: 0.187919 seconds
% 0.13/0.44 % Total memory used: 108.787 MB
% 0.13/0.44 % Net memory used: 108.617 MB
%------------------------------------------------------------------------------