%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC118+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 : n003.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 02:40:02 PM UTC 2026
% Result : Theorem 0.07s 0.37s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 79 ( 15 unt; 12 def)
% Number of atoms : 336 ( 84 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 402 ( 145 ~; 142 |; 83 &)
% ( 16 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 13 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 97 ( 63 !; 34 ?)
% 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(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( segmentP(V,U)
& neq(U,nil) )
| ( nil = U
& nil = V )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( leq(X7,X5)
& app(X8,cons(X7,nil)) = W
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = Z
& ssList(X6) )
& ssItem(X5) )
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( leq(X1,X3)
& app(cons(X3,nil),X4) = W
& ssList(X4) )
& ssItem(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ totalorderedP(W)
| app(app(Y,W),Z) != X ) ) )
| 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)
=> ( ( segmentP(V,U)
& neq(U,nil) )
| ( nil = U
& nil = V )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( leq(X7,X5)
& app(X8,cons(X7,nil)) = W
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = Z
& ssList(X6) )
& ssItem(X5) )
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( leq(X1,X3)
& app(cons(X3,nil),X4) = W
& ssList(X4) )
& ssItem(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ totalorderedP(W)
| app(app(Y,W),Z) != X ) ) )
| 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(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ segmentP(V,U)
| ~ neq(U,nil) )
& ( nil != U
| nil != V )
& ( nil != W
| nil = X )
& ? [Y] :
( ? [Z] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ leq(X7,X5)
| app(X8,cons(X7,nil)) != W
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != Z
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ~ leq(X1,X3)
| app(cons(X3,nil),X4) != W
| ~ ssList(X4) )
| ~ ssItem(X3) )
| app(X2,cons(X1,nil)) != Y
| ~ ssList(X2) )
| ~ ssItem(X1) )
& totalorderedP(W)
& app(app(Y,W),Z) = X
& ssList(Z) )
& 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] :
( ( ~ segmentP(V,U)
| ~ neq(U,nil) )
& ( nil != U
| nil != V )
& ( nil != W
| nil = X )
& ? [Y] :
( ? [Z] :
( ! [X5] :
( ! [X7] :
( ~ leq(X7,X5)
| ! [X8] :
( app(X8,cons(X7,nil)) != W
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ! [X6] :
( app(cons(X5,nil),X6) != Z
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X1] :
( ! [X3] :
( ~ leq(X1,X3)
| ! [X4] :
( app(cons(X3,nil),X4) != W
| ~ ssList(X4) )
| ~ ssItem(X3) )
| ! [X2] :
( app(X2,cons(X1,nil)) != Y
| ~ ssList(X2) )
| ~ ssItem(X1) )
& totalorderedP(W)
& app(app(Y,W),Z) = X
& ssList(Z) )
& ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(miniscoping,[status(thm)],[f415]) ).
fof(f417,plain,
( ( ~ segmentP(sK48_skl,sK47_skl)
| ~ neq(sK47_skl,nil) )
& ( nil != sK47_skl
| nil != sK48_skl )
& ( nil != sK49_skl
| nil = sK50_skl )
& ! [X5] :
( ! [X7] :
( ~ leq(X7,X5)
| ! [X8] :
( app(X8,cons(X7,nil)) != sK49_skl
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ! [X6] :
( app(cons(X5,nil),X6) != sK52_skl
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X1] :
( ! [X3] :
( ~ leq(X1,X3)
| ! [X4] :
( app(cons(X3,nil),X4) != sK49_skl
| ~ ssList(X4) )
| ~ ssItem(X3) )
| ! [X2] :
( app(X2,cons(X1,nil)) != sK51_skl
| ~ ssList(X2) )
| ~ ssItem(X1) )
& totalorderedP(sK49_skl)
& app(app(sK51_skl,sK49_skl),sK52_skl) = sK50_skl
& ssList(sK52_skl)
& ssList(sK51_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,sK52_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl),skolemize(Z,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,
ssList(sK51_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f425,plain,
ssList(sK52_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f426,plain,
app(app(sK51_skl,sK49_skl),sK52_skl) = sK50_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f430,plain,
( nil != sK49_skl
| nil = sK50_skl ),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f431,plain,
( nil != sK47_skl
| nil != sK48_skl ),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f432,plain,
( ~ segmentP(sK48_skl,sK47_skl)
| ~ neq(sK47_skl,nil) ),
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)],[f430,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)],[f431,f440,f443]) ).
fof(f447,definition,
( sQ4_spl
<=> neq(sK47_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f449,plain,
( sQ4_spl
| ~ neq(sK47_skl,nil) ),
inference(component_clause,[status(thm)],[f447]) ).
fof(f450,definition,
( sQ5_spl
<=> segmentP(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f452,plain,
( sQ5_spl
| ~ segmentP(sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f450]) ).
fof(f453,plain,
( ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f432,f447,f450]) ).
fof(f460,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(f486,plain,
( sQ2_spl
| nil != sK50_skl ),
inference(forward_demodulation,[status(thm)],[f422,f442]) ).
fof(f487,plain,
( ~ sQ0_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f434,f486]) ).
fof(f488,plain,
( ~ sQ0_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f487]) ).
fof(f489,plain,
( sQ3_spl
| nil != sK49_skl ),
inference(forward_demodulation,[status(thm)],[f423,f445]) ).
fof(f502,plain,
( sQ4_spl
| ~ neq(sK49_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f423,f449]) ).
fof(f515,plain,
( sQ5_spl
| ~ segmentP(sK50_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f422,f452]) ).
fof(f516,plain,
( sQ5_spl
| ~ segmentP(sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f515]) ).
fof(f518,plain,
( ~ ssList(sK52_skl)
| ~ ssList(sK51_skl)
| segmentP(sK50_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(app(app(sK51_skl,sK49_skl),sK52_skl)) ),
inference(paramodulation,[status(thm)],[f426,f460]) ).
fof(f520,definition,
( sQ9_spl
<=> ssList(app(app(sK51_skl,sK49_skl),sK52_skl)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f522,plain,
( sQ9_spl
| ~ ssList(app(app(sK51_skl,sK49_skl),sK52_skl)) ),
inference(component_clause,[status(thm)],[f520]) ).
fof(f523,definition,
( sQ10_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f525,plain,
( sQ10_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f523]) ).
fof(f526,definition,
( sQ11_spl
<=> segmentP(sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f527,plain,
( ~ sQ11_spl
| segmentP(sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f526]) ).
fof(f529,definition,
( sQ12_spl
<=> ssList(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f531,plain,
( sQ12_spl
| ~ ssList(sK51_skl) ),
inference(component_clause,[status(thm)],[f529]) ).
fof(f532,definition,
( sQ13_spl
<=> ssList(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f534,plain,
( sQ13_spl
| ~ ssList(sK52_skl) ),
inference(component_clause,[status(thm)],[f532]) ).
fof(f535,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f518,f520,f523,f526,f529,f532]) ).
fof(f543,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f534,f425]) ).
fof(f544,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f543]) ).
fof(f546,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f531,f424]) ).
fof(f547,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f546]) ).
fof(f548,plain,
( ~ sQ11_spl
| sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f527,f516]) ).
fof(f549,plain,
( ~ sQ11_spl
| sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f548]) ).
fof(f550,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f525,f420]) ).
fof(f551,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f550]) ).
fof(f554,plain,
( sQ9_spl
| ~ ssList(sK50_skl) ),
inference(forward_demodulation,[status(thm)],[f426,f522]) ).
fof(f555,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f554,f421]) ).
fof(f556,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f555]) ).
fof(f564,definition,
( sQ17_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f566,plain,
( sQ17_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f564]) ).
fof(f581,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f566,f223]) ).
fof(f582,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f581]) ).
fof(f585,plain,
( sQ4_spl
| sK49_skl = nil
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f220,f502]) ).
fof(f588,plain,
( sQ4_spl
| sQ1_spl
| ~ sQ17_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f585,f523,f564,f436,f447]) ).
fof(f589,plain,
( sQ3_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f489,f436,f443]) ).
fof(f590,plain,
$false,
inference(sat_refutation,[status(thm)],[f439,f446,f453,f488,f535,f544,f547,f549,f551,f556,f582,f588,f589]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC118+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n003.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 07:59:00 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.37 % Drodi V4.1.1
% 0.07/0.37 % Refutation found
% 0.07/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.40 % Elapsed time: 0.045799 seconds
% 0.14/0.40 % CPU time: 0.093269 seconds
% 0.14/0.40 % Total memory used: 20.996 MB
% 0.14/0.40 % Net memory used: 20.967 MB
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