%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC076+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 : n005.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 02:39:52 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 83 ( 15 unt; 12 def)
% Number of atoms : 356 ( 88 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 440 ( 167 ~; 161 |; 79 &)
% ( 16 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 13 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 102 ( 70 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( nil = U
& nil = V )
| ( nil = W
& nil != X )
| ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(X7,cons(X5,nil)) = W
& ssList(X7) )
& app(cons(X5,nil),X6) = X1
& ssList(X6) )
& ssItem(X5) )
| ? [X2] :
( ? [X3] :
( ? [X4] :
( app(cons(X2,nil),X4) = W
& ssList(X4) )
& app(X3,cons(X2,nil)) = Z
& ssList(X3) )
& ssItem(X2) )
| ~ equalelemsP(W)
| app(app(Z,W),X1) != X ) ) )
| ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( nil = U
& nil = V )
| ( nil = W
& nil != X )
| ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(X7,cons(X5,nil)) = W
& ssList(X7) )
& app(cons(X5,nil),X6) = X1
& ssList(X6) )
& ssItem(X5) )
| ? [X2] :
( ? [X3] :
( ? [X4] :
( app(cons(X2,nil),X4) = W
& ssList(X4) )
& app(X3,cons(X2,nil)) = Z
& ssList(X3) )
& ssItem(X2) )
| ~ equalelemsP(W)
| app(app(Z,W),X1) != X ) ) )
| ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f131,plain,
! [U] :
( ! [V] :
( ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f132,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ( app(app(sK7_skl(V,U),V),sK8_skl(V,U)) = U
& ssList(sK8_skl(V,U))
& ssList(sK7_skl(V,U)) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
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(f318,plain,
! [U] :
( segmentP(U,U)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f55]) ).
fof(f319,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f318]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( nil != U
| nil != V )
& ( nil != W
| nil = X )
& ? [Z] :
( ? [X1] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != W
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X1
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X2] :
( ! [X3] :
( ! [X4] :
( app(cons(X2,nil),X4) != W
| ~ ssList(X4) )
| app(X3,cons(X2,nil)) != Z
| ~ ssList(X3) )
| ~ ssItem(X2) )
& equalelemsP(W)
& app(app(Z,W),X1) = X
& ssList(X1) )
& ssList(Z) )
& ! [Y] :
( ~ segmentP(U,Y)
| ~ segmentP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( nil != U
| nil != V )
& ( nil != W
| nil = X )
& ? [Z] :
( ? [X1] :
( ! [X5] :
( ! [X7] :
( app(X7,cons(X5,nil)) != W
| ~ ssList(X7) )
| ! [X6] :
( app(cons(X5,nil),X6) != X1
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X2] :
( ! [X4] :
( app(cons(X2,nil),X4) != W
| ~ ssList(X4) )
| ! [X3] :
( app(X3,cons(X2,nil)) != Z
| ~ ssList(X3) )
| ~ ssItem(X2) )
& equalelemsP(W)
& app(app(Z,W),X1) = X
& ssList(X1) )
& ssList(Z) )
& ! [Y] :
( ~ segmentP(U,Y)
| ~ segmentP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(miniscoping,[status(thm)],[f415]) ).
fof(f417,plain,
( ( nil != sK47_skl
| nil != sK48_skl )
& ( nil != sK49_skl
| nil = sK50_skl )
& ! [X5] :
( ! [X7] :
( app(X7,cons(X5,nil)) != sK49_skl
| ~ ssList(X7) )
| ! [X6] :
( app(cons(X5,nil),X6) != sK52_skl
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X2] :
( ! [X4] :
( app(cons(X2,nil),X4) != sK49_skl
| ~ ssList(X4) )
| ! [X3] :
( app(X3,cons(X2,nil)) != sK51_skl
| ~ ssList(X3) )
| ~ ssItem(X2) )
& equalelemsP(sK49_skl)
& app(app(sK51_skl,sK49_skl),sK52_skl) = sK50_skl
& ssList(sK52_skl)
& ssList(sK51_skl)
& ! [Y] :
( ~ segmentP(sK47_skl,Y)
| ~ segmentP(sK48_skl,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& 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,sK52_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Z,sK51_skl),skolemize(X1,sK52_skl)],[f416]) ).
fof(f420,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f421,plain,
ssList(sK50_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f422,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f423,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f424,plain,
! [X0] :
( ~ segmentP(sK47_skl,X0)
| ~ segmentP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f425,plain,
ssList(sK51_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f426,plain,
ssList(sK52_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f427,plain,
app(app(sK51_skl,sK49_skl),sK52_skl) = sK50_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f431,plain,
( nil != sK49_skl
| nil = sK50_skl ),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f432,plain,
( nil != sK47_skl
| nil != sK48_skl ),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f433,definition,
( sQ0_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f434,plain,
( ~ sQ0_spl
| nil = sK50_skl ),
inference(component_clause,[status(thm)],[f433]) ).
fof(f436,definition,
( sQ1_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f439,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f431,f433,f436]) ).
fof(f440,definition,
( sQ2_spl
<=> nil = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( sQ2_spl
| nil != sK48_skl ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f443,definition,
( sQ3_spl
<=> nil = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f445,plain,
( sQ3_spl
| nil != sK47_skl ),
inference(component_clause,[status(thm)],[f443]) ).
fof(f446,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f432,f440,f443]) ).
fof(f453,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X0)
| segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f137]) ).
fof(f479,plain,
( sQ2_spl
| nil != sK50_skl ),
inference(forward_demodulation,[status(thm)],[f422,f442]) ).
fof(f480,plain,
( ~ sQ0_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f434,f479]) ).
fof(f481,plain,
( ~ sQ0_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f480]) ).
fof(f482,plain,
( sQ3_spl
| nil != sK49_skl ),
inference(forward_demodulation,[status(thm)],[f423,f445]) ).
fof(f503,definition,
( sQ4_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f505,plain,
( sQ4_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f503]) ).
fof(f506,definition,
( sQ5_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f508,plain,
( sQ5_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f506]) ).
fof(f509,definition,
( sQ6_spl
<=> segmentP(app(app(sK51_skl,sK49_skl),sK52_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f510,plain,
( ~ sQ6_spl
| segmentP(app(app(sK51_skl,sK49_skl),sK52_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f509]) ).
fof(f512,definition,
( sQ7_spl
<=> ssList(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f514,plain,
( sQ7_spl
| ~ ssList(sK51_skl) ),
inference(component_clause,[status(thm)],[f512]) ).
fof(f515,definition,
( sQ8_spl
<=> ssList(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f517,plain,
( sQ8_spl
| ~ ssList(sK52_skl) ),
inference(component_clause,[status(thm)],[f515]) ).
fof(f534,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f517,f426]) ).
fof(f535,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f534]) ).
fof(f536,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f505,f223]) ).
fof(f537,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f536]) ).
fof(f538,plain,
! [X0] :
( ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f423,f424]) ).
fof(f539,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f514,f425]) ).
fof(f540,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f539]) ).
fof(f549,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f508,f420]) ).
fof(f550,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f549]) ).
fof(f556,definition,
( sQ15_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f558,plain,
( sQ15_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f556]) ).
fof(f561,plain,
( ~ ssList(sK52_skl)
| ~ ssList(sK51_skl)
| segmentP(app(app(sK51_skl,sK49_skl),sK52_skl),sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f427,f453]) ).
fof(f563,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| sQ6_spl
| ~ sQ5_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f561,f556,f506,f509,f512,f515]) ).
fof(f568,plain,
( ~ sQ6_spl
| segmentP(sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f427,f510]) ).
fof(f569,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f558,f421]) ).
fof(f570,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f569]) ).
fof(f659,plain,
! [X0] :
( ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f422,f538]) ).
fof(f660,plain,
! [X0] :
( X0 = nil
| ~ ssList(nil)
| ~ ssList(X0)
| ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f659,f220]) ).
fof(f661,definition,
! [X0] :
( sQ32_spl
<=> ( X0 = nil
| ~ ssList(X0)
| ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f662,plain,
! [X0] :
( ~ sQ32_spl
| X0 = nil
| ~ ssList(X0)
| ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f661]) ).
fof(f664,plain,
( ~ sQ4_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f660,f661,f503]) ).
fof(f665,plain,
! [X0] :
( ~ sQ32_spl
| X0 = nil
| ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f662]) ).
fof(f667,plain,
( ~ sQ32_spl
| ~ ssList(sK49_skl)
| sK49_skl = nil
| ~ segmentP(sK50_skl,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f665,f319]) ).
fof(f675,definition,
( sQ35_spl
<=> segmentP(sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f677,plain,
( sQ35_spl
| ~ segmentP(sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f675]) ).
fof(f678,plain,
( ~ sQ32_spl
| sQ1_spl
| ~ sQ35_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f667,f506,f675,f436,f661]) ).
fof(f679,plain,
( sQ35_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f677,f568]) ).
fof(f680,plain,
( sQ35_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f679]) ).
fof(f681,plain,
( sQ3_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f482,f436,f443]) ).
fof(f684,plain,
$false,
inference(sat_refutation,[status(thm)],[f439,f446,f481,f535,f537,f540,f550,f563,f570,f664,f678,f680,f681]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC076+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n005.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 07:53:18 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.055624 seconds
% 0.13/0.42 % CPU time: 0.180099 seconds
% 0.13/0.42 % Total memory used: 111.479 MB
% 0.13/0.42 % Net memory used: 111.262 MB
%------------------------------------------------------------------------------