%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC275+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 : n013.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 02:40:36 PM UTC 2026
% Result : Theorem 0.14s 10.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 53 ( 13 unt; 8 def)
% Number of atoms : 153 ( 35 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 160 ( 60 ~; 56 |; 25 &)
% ( 10 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 9 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 26 ( 21 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,axiom,
! [U] :
( ssItem(U)
=> totalorderedP(cons(U,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( neq(X,nil)
& ! [Y] :
( ~ memberP(X,Y)
| cons(Y,nil) != W
| ~ ssItem(Y) ) )
| ( nil = X
& nil != W )
| totalorderedP(U)
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( neq(X,nil)
& ! [Y] :
( ~ memberP(X,Y)
| cons(Y,nil) != W
| ~ ssItem(Y) ) )
| ( nil = X
& nil != W )
| totalorderedP(U)
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f217,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f218,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f217]) ).
fof(f220,plain,
! [X0,X1] :
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f337,plain,
! [U] :
( totalorderedP(cons(U,nil))
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f65]) ).
fof(f338,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f337]) ).
fof(f339,plain,
totalorderedP(nil),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ neq(X,nil)
| ? [Y] :
( memberP(X,Y)
& cons(Y,nil) = W
& ssItem(Y) ) )
& ( nil != X
| nil = W )
& ~ totalorderedP(U)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( ( ~ neq(sK50_skl,nil)
| ( memberP(sK50_skl,sK51_skl)
& cons(sK51_skl,nil) = sK49_skl
& ssItem(sK51_skl) ) )
& ( nil != sK50_skl
| nil = sK49_skl )
& ~ totalorderedP(sK47_skl)
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& ssList(sK50_skl)
& ssList(sK49_skl)
& ssList(sK48_skl)
& ssList(sK47_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl,sK51_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl)],[f415]) ).
fof(f420,plain,
ssList(sK50_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f422,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f423,plain,
~ totalorderedP(sK47_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
( nil != sK50_skl
| nil = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f425,plain,
( ~ neq(sK50_skl,nil)
| ssItem(sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f426,plain,
( ~ neq(sK50_skl,nil)
| cons(sK51_skl,nil) = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f428,definition,
( sQ0_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f429,plain,
( ~ sQ0_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f428]) ).
fof(f431,definition,
( sQ1_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f434,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f424,f428,f431]) ).
fof(f435,definition,
( sQ2_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f438,definition,
( sQ3_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f440,plain,
( sQ3_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f441,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f425,f435,f438]) ).
fof(f442,definition,
( sQ4_spl
<=> cons(sK51_skl,nil) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( ~ sQ4_spl
| cons(sK51_skl,nil) = sK49_skl ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f426,f442,f438]) ).
fof(f482,plain,
~ totalorderedP(sK49_skl),
inference(forward_demodulation,[status(thm)],[f422,f423]) ).
fof(f483,plain,
( ~ sQ0_spl
| totalorderedP(sK49_skl) ),
inference(backward_demodulation,[status(thm)],[f429,f339]) ).
fof(f485,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f483,f482]) ).
fof(f486,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f485]) ).
fof(f497,plain,
( sQ3_spl
| sK50_skl = nil
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f220,f440]) ).
fof(f500,definition,
( sQ8_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f502,plain,
( sQ8_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f500]) ).
fof(f503,definition,
( sQ9_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f505,plain,
( sQ9_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f503]) ).
fof(f506,plain,
( sQ3_spl
| sQ1_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f497,f500,f503,f431,f438]) ).
fof(f507,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f505,f223]) ).
fof(f508,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f507]) ).
fof(f509,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f502,f420]) ).
fof(f510,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f509]) ).
fof(f511,plain,
( ~ sQ4_spl
| totalorderedP(sK49_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f443,f338]) ).
fof(f514,definition,
( sQ10_spl
<=> totalorderedP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f515,plain,
( ~ sQ10_spl
| totalorderedP(sK49_skl) ),
inference(component_clause,[status(thm)],[f514]) ).
fof(f517,plain,
( ~ sQ4_spl
| sQ10_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f511,f435,f514,f442]) ).
fof(f523,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f515,f482]) ).
fof(f524,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f523]) ).
fof(f525,plain,
$false,
inference(sat_refutation,[status(thm)],[f434,f441,f445,f486,f506,f508,f510,f517,f524]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC275+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.38 % Computer : n013.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Mon Sep 21 08:10:32 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.39 % Drodi V4.1.1
% 0.14/10.41 % Refutation found
% 0.14/10.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/10.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/10.44 % Elapsed time: 0.050272 seconds
% 0.14/10.44 % CPU time: 0.158702 seconds
% 0.14/10.44 % Total memory used: 110.291 MB
% 0.14/10.44 % Net memory used: 110.151 MB
%------------------------------------------------------------------------------