%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC181-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 02:40:17 PM UTC 2026
% Result : Unsatisfiable 27.01s 4.34s
% Output : CNFRefutation 27.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 21
% Syntax : Number of formulae : 73 ( 22 unt; 10 def)
% Number of atoms : 184 ( 10 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 207 ( 96 ~; 101 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 17 ( 15 usr; 11 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 54 ( 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [U] : ssList(skaf77(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [U] : ssList(skaf76(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [U] : ssList(skaf75(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,axiom,
! [U] :
( ~ ssItem(U)
| ~ lt(U,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f72,axiom,
! [U,V] :
( ssItem(V)
| duplicatefreeP(U)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f162,axiom,
! [U] :
( app(app(skaf75(U),cons(skaf74(U),skaf76(U))),cons(skaf74(U),skaf77(U))) = U
| duplicatefreeP(U)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f181,axiom,
! [U,V,W,X,Y,Z] :
( lt(V,X)
| ~ ssList(Z)
| ~ strictorderedP(Z)
| ~ ssItem(V)
| ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssList(Y)
| app(app(U,cons(V,W)),cons(X,Y)) != Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f186,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
strictorderedP(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
~ duplicatefreeP(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f217,plain,
! [X0] : ssList(skaf77(X0)),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f218,plain,
! [X0] : ssList(skaf76(X0)),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f219,plain,
! [X0] : ssList(skaf75(X0)),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f262,plain,
! [X0] :
( ~ ssItem(X0)
| ~ lt(X0,X0) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f271,plain,
( ! [V] : ssItem(V)
| ! [U] :
( duplicatefreeP(U)
| ~ ssList(U) ) ),
inference(miniscoping,[status(thm)],[f72]) ).
fof(f272,plain,
! [X0,X1] :
( ssItem(X1)
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f271]) ).
fof(f392,plain,
! [X0] :
( app(app(skaf75(X0),cons(skaf74(X0),skaf76(X0))),cons(skaf74(X0),skaf77(X0))) = X0
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f420,plain,
! [V,X] :
( lt(V,X)
| ! [Z] :
( ~ ssList(Z)
| ~ strictorderedP(Z)
| ~ ssItem(V)
| ~ ssItem(X)
| ! [U] :
( ~ ssList(U)
| ! [W] :
( ~ ssList(W)
| ! [Y] :
( ~ ssList(Y)
| app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) ) ) ),
inference(miniscoping,[status(thm)],[f181]) ).
fof(f421,plain,
! [X0,X1,X2,X3,X4,X5] :
( lt(X1,X3)
| ~ ssList(X5)
| ~ strictorderedP(X5)
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X4)
| app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
inference(cnf_transformation,[status(thm)],[f420]) ).
fof(f430,plain,
ssList(sk1),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f435,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f439,plain,
strictorderedP(sk3),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f444,plain,
~ duplicatefreeP(sk1),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f446,definition,
! [X0] :
( sQ0_spl
<=> ( duplicatefreeP(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f447,plain,
! [X0] :
( ~ sQ0_spl
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f449,definition,
! [X1] :
( sQ1_spl
<=> ssItem(X1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f450,plain,
! [X0] :
( ~ sQ1_spl
| ssItem(X0) ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f452,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f272,f446,f449]) ).
fof(f486,plain,
! [X0,X1,X2,X3,X4] :
( lt(X4,X3)
| ~ ssList(app(app(X2,cons(X4,X1)),cons(X3,X0)))
| ~ strictorderedP(app(app(X2,cons(X4,X1)),cons(X3,X0)))
| ~ ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f421]) ).
fof(f495,plain,
strictorderedP(sk1),
inference(forward_demodulation,[status(thm)],[f435,f439]) ).
fof(f600,plain,
( ~ sQ0_spl
| duplicatefreeP(sk1) ),
inference(resolution,[status(thm)],[f447,f430]) ).
fof(f601,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f600,f444]) ).
fof(f602,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f601]) ).
fof(f604,plain,
! [X0] :
( ~ sQ1_spl
| ~ lt(X0,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f262,f450]) ).
fof(f627,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| lt(X4,X3)
| ~ ssList(app(app(X2,cons(X4,X1)),cons(X3,X0)))
| ~ strictorderedP(app(app(X2,cons(X4,X1)),cons(X3,X0)))
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f486,f450]) ).
fof(f673,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| lt(X3,X4)
| ~ ssList(app(app(X2,cons(X3,X1)),cons(X4,X0)))
| ~ strictorderedP(app(app(X2,cons(X3,X1)),cons(X4,X0)))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f627,f450]) ).
fof(f894,definition,
( sQ17_spl
<=> ssList(sk1) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f896,plain,
( sQ17_spl
| ~ ssList(sk1) ),
inference(component_clause,[status(thm)],[f894]) ).
fof(f900,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f896,f430]) ).
fof(f901,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f900]) ).
fof(f4280,plain,
( app(app(skaf75(sk1),cons(skaf74(sk1),skaf76(sk1))),cons(skaf74(sk1),skaf77(sk1))) = sk1
| duplicatefreeP(sk1) ),
inference(resolution,[status(thm)],[f392,f430]) ).
fof(f4328,definition,
( sQ203_spl
<=> duplicatefreeP(sk1) ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f4329,plain,
( ~ sQ203_spl
| duplicatefreeP(sk1) ),
inference(component_clause,[status(thm)],[f4328]) ).
fof(f4331,definition,
( sQ204_spl
<=> app(app(skaf75(sk1),cons(skaf74(sk1),skaf76(sk1))),cons(skaf74(sk1),skaf77(sk1))) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f4332,plain,
( ~ sQ204_spl
| app(app(skaf75(sk1),cons(skaf74(sk1),skaf76(sk1))),cons(skaf74(sk1),skaf77(sk1))) = sk1 ),
inference(component_clause,[status(thm)],[f4331]) ).
fof(f4334,plain,
( sQ204_spl
| sQ203_spl ),
inference(split_clause,[status(thm)],[f4280,f4328,f4331]) ).
fof(f4363,plain,
( ~ sQ203_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4329,f444]) ).
fof(f4364,plain,
~ sQ203_spl,
inference(contradiction_clause,[status(thm)],[f4363]) ).
fof(f5403,plain,
( ~ sQ204_spl
| ~ sQ1_spl
| lt(skaf74(sk1),skaf74(sk1))
| ~ ssList(sk1)
| ~ strictorderedP(app(app(skaf75(sk1),cons(skaf74(sk1),skaf76(sk1))),cons(skaf74(sk1),skaf77(sk1))))
| ~ ssList(skaf75(sk1))
| ~ ssList(skaf76(sk1))
| ~ ssList(skaf77(sk1)) ),
inference(paramodulation,[status(thm)],[f4332,f673]) ).
fof(f5411,definition,
( sQ261_spl
<=> ssList(skaf77(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f5413,plain,
( sQ261_spl
| ~ ssList(skaf77(sk1)) ),
inference(component_clause,[status(thm)],[f5411]) ).
fof(f5414,definition,
( sQ262_spl
<=> ssList(skaf76(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition]) ).
fof(f5416,plain,
( sQ262_spl
| ~ ssList(skaf76(sk1)) ),
inference(component_clause,[status(thm)],[f5414]) ).
fof(f5417,definition,
( sQ263_spl
<=> ssList(skaf75(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ263_spl])],[split_symbol_definition]) ).
fof(f5419,plain,
( sQ263_spl
| ~ ssList(skaf75(sk1)) ),
inference(component_clause,[status(thm)],[f5417]) ).
fof(f5438,definition,
( sQ269_spl
<=> lt(skaf74(sk1),skaf74(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f5439,plain,
( ~ sQ269_spl
| lt(skaf74(sk1),skaf74(sk1)) ),
inference(component_clause,[status(thm)],[f5438]) ).
fof(f5446,definition,
( sQ271_spl
<=> strictorderedP(app(app(skaf75(sk1),cons(skaf74(sk1),skaf76(sk1))),cons(skaf74(sk1),skaf77(sk1)))) ),
introduced(definition,[new_symbols(definition,[sQ271_spl])],[split_symbol_definition]) ).
fof(f5448,plain,
( sQ271_spl
| ~ strictorderedP(app(app(skaf75(sk1),cons(skaf74(sk1),skaf76(sk1))),cons(skaf74(sk1),skaf77(sk1)))) ),
inference(component_clause,[status(thm)],[f5446]) ).
fof(f5449,plain,
( ~ sQ204_spl
| ~ sQ1_spl
| sQ269_spl
| ~ sQ17_spl
| ~ sQ271_spl
| ~ sQ263_spl
| ~ sQ262_spl
| ~ sQ261_spl ),
inference(split_clause,[status(thm)],[f5403,f5411,f5414,f5417,f5446,f894,f5438,f449,f4331]) ).
fof(f5484,plain,
( sQ261_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5413,f217]) ).
fof(f5485,plain,
sQ261_spl,
inference(contradiction_clause,[status(thm)],[f5484]) ).
fof(f5486,plain,
( sQ263_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5419,f219]) ).
fof(f5487,plain,
sQ263_spl,
inference(contradiction_clause,[status(thm)],[f5486]) ).
fof(f5488,plain,
( sQ262_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5416,f218]) ).
fof(f5489,plain,
sQ262_spl,
inference(contradiction_clause,[status(thm)],[f5488]) ).
fof(f5490,plain,
( ~ sQ269_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5439,f604]) ).
fof(f5491,plain,
( ~ sQ269_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f5490]) ).
fof(f5504,plain,
( sQ271_spl
| ~ sQ204_spl
| ~ strictorderedP(sk1) ),
inference(forward_demodulation,[status(thm)],[f4332,f5448]) ).
fof(f5505,plain,
( sQ271_spl
| ~ sQ204_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5504,f495]) ).
fof(f5506,plain,
( sQ271_spl
| ~ sQ204_spl ),
inference(contradiction_clause,[status(thm)],[f5505]) ).
fof(f5507,plain,
$false,
inference(sat_refutation,[status(thm)],[f452,f602,f901,f4334,f4364,f5449,f5485,f5487,f5489,f5491,f5506]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC181-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n002.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 08:04:46 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.50 % Drodi V4.1.1
% 27.01/4.34 % Refutation found
% 27.01/4.34 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 27.01/4.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.17/4.42 % Elapsed time: 3.945622 seconds
% 4.17/4.42 % CPU time: 30.636461 seconds
% 4.17/4.42 % Total memory used: 269.418 MB
% 4.17/4.42 % Net memory used: 255.632 MB
%------------------------------------------------------------------------------