%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC069-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 02:39:50 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.38s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 31
% Syntax : Number of formulae : 86 ( 14 unt; 15 def)
% Number of atoms : 197 ( 32 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 208 ( 97 ~; 96 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 16 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 18 ( 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [U] :
( segmentP(U,nil)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f79,axiom,
! [U] :
( segmentP(nil,U)
| ~ ssList(U)
| nil != U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f100,axiom,
! [U,V] :
( V = U
| neq(V,U)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f127,axiom,
! [U,V] :
( V = U
| ~ ssList(V)
| ~ ssList(U)
| ~ segmentP(V,U)
| ~ segmentP(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f188,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f189,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f190,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
! [A] :
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
( nil != sk4
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
( nil != sk1
| nil != sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
( ~ neq(sk4,nil)
| neq(sk5,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( ~ neq(sk4,nil)
| segmentP(sk4,sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
( ~ neq(sk4,nil)
| segmentP(sk3,sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f206,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f254,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f278,plain,
! [X0] :
( segmentP(nil,X0)
| ~ ssList(X0)
| nil != X0 ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f301,plain,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f338,plain,
! [X0,X1] :
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
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,
! [X0] :
( ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f436,plain,
( nil != sk4
| nil = sk3 ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f437,plain,
( nil != sk1
| nil != sk2 ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f438,plain,
( ~ neq(sk4,nil)
| ssList(sk5) ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f439,plain,
( ~ neq(sk4,nil)
| neq(sk5,nil) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f440,plain,
( ~ neq(sk4,nil)
| segmentP(sk4,sk5) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f441,plain,
( ~ neq(sk4,nil)
| segmentP(sk3,sk5) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f449,definition,
( sQ2_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f452,definition,
( sQ3_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f453,plain,
( ~ sQ3_spl
| nil = sk4 ),
inference(component_clause,[status(thm)],[f452]) ).
fof(f455,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f436,f449,f452]) ).
fof(f456,definition,
( sQ4_spl
<=> nil = sk2 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f458,plain,
( sQ4_spl
| nil != sk2 ),
inference(component_clause,[status(thm)],[f456]) ).
fof(f459,definition,
( sQ5_spl
<=> nil = sk1 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f461,plain,
( sQ5_spl
| nil != sk1 ),
inference(component_clause,[status(thm)],[f459]) ).
fof(f462,plain,
( ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f437,f456,f459]) ).
fof(f463,definition,
( sQ6_spl
<=> ssList(sk5) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f466,definition,
( sQ7_spl
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f468,plain,
( sQ7_spl
| ~ neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f466]) ).
fof(f469,plain,
( ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f438,f463,f466]) ).
fof(f470,definition,
( sQ8_spl
<=> neq(sk5,nil) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f473,plain,
( ~ sQ7_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f439,f470,f466]) ).
fof(f474,definition,
( sQ9_spl
<=> segmentP(sk4,sk5) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f475,plain,
( ~ sQ9_spl
| segmentP(sk4,sk5) ),
inference(component_clause,[status(thm)],[f474]) ).
fof(f477,plain,
( ~ sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f440,f474,f466]) ).
fof(f478,definition,
( sQ10_spl
<=> segmentP(sk3,sk5) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f481,plain,
( ~ sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f441,f478,f466]) ).
fof(f482,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(destructive_equality_resolution,[status(thm)],[f278]) ).
fof(f513,plain,
( sQ4_spl
| nil != sk4 ),
inference(forward_demodulation,[status(thm)],[f433,f458]) ).
fof(f525,definition,
( sQ11_spl
<=> ssList(sk3) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f527,plain,
( sQ11_spl
| ~ ssList(sk3) ),
inference(component_clause,[status(thm)],[f525]) ).
fof(f533,definition,
( sQ13_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f535,plain,
( sQ13_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f533]) ).
fof(f536,definition,
( sQ14_spl
<=> segmentP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f537,plain,
( ~ sQ14_spl
| segmentP(nil,nil) ),
inference(component_clause,[status(thm)],[f536]) ).
fof(f539,plain,
( sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f482,f533,f536]) ).
fof(f542,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f535,f206]) ).
fof(f543,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f542]) ).
fof(f544,plain,
( sQ7_spl
| sk4 = nil
| ~ ssList(sk4)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f468,f301]) ).
fof(f545,definition,
( sQ15_spl
<=> ssList(sk4) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f547,plain,
( sQ15_spl
| ~ ssList(sk4) ),
inference(component_clause,[status(thm)],[f545]) ).
fof(f548,plain,
( sQ7_spl
| sQ3_spl
| ~ sQ15_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f544,f533,f545,f452,f466]) ).
fof(f549,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f547,f432]) ).
fof(f550,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f549]) ).
fof(f551,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f527,f431]) ).
fof(f552,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f551]) ).
fof(f582,plain,
! [X0] :
( ~ segmentP(sk1,X0)
| ~ segmentP(sk4,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f433,f435]) ).
fof(f583,plain,
! [X0] :
( ~ segmentP(sk3,X0)
| ~ segmentP(sk4,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f434,f582]) ).
fof(f588,plain,
( ~ sQ14_spl
| nil = nil
| ~ ssList(nil)
| ~ ssList(nil)
| ~ segmentP(nil,nil) ),
inference(resolution,[status(thm)],[f338,f537]) ).
fof(f589,plain,
! [X0] :
( ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(nil,X0) ),
inference(resolution,[status(thm)],[f338,f254]) ).
fof(f605,definition,
( sQ24_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f608,plain,
( sQ24_spl
| ~ sQ13_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f588,f536,f533,f605]) ).
fof(f609,definition,
! [X0] :
( sQ25_spl
<=> ( ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f612,plain,
( ~ sQ13_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f589,f609,f533]) ).
fof(f614,plain,
( ~ sQ9_spl
| ~ segmentP(sk3,sk5)
| ~ neq(sk5,nil)
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[f583,f475]) ).
fof(f620,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f614,f463,f470,f478,f474]) ).
fof(f638,plain,
( sQ5_spl
| nil != sk3 ),
inference(forward_demodulation,[status(thm)],[f434,f461]) ).
fof(f639,plain,
( ~ sQ3_spl
| sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f453,f513]) ).
fof(f640,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f639]) ).
fof(f654,plain,
( sQ5_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f638,f449,f459]) ).
fof(f655,plain,
$false,
inference(sat_refutation,[status(thm)],[f455,f462,f469,f473,f477,f481,f539,f543,f548,f550,f552,f608,f612,f620,f640,f654]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC069-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 07:51:05 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 0.15/0.38 % Refutation found
% 0.15/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.42 % Elapsed time: 0.050182 seconds
% 0.15/0.42 % CPU time: 0.099399 seconds
% 0.15/0.42 % Total memory used: 24.037 MB
% 0.15/0.42 % Net memory used: 24.008 MB
%------------------------------------------------------------------------------