%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC012+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 02:39:35 PM UTC 2026
% Result : Theorem 95.10s 12.54s
% Output : CNFRefutation 95.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 27
% Syntax : Number of formulae : 121 ( 15 unt; 21 def)
% Number of atoms : 446 ( 69 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 560 ( 235 ~; 212 |; 72 &)
% ( 25 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 21 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-4 aty)
% Number of variables : 204 ( 174 !; 30 ?)
% 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(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [X2] :
( ssItem(X2)
=> app(W,cons(X2,nil)) != X )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Z,X1) = U
& app(app(Z,cons(Y,nil)),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| ~ neq(V,nil) ) )
| 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)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [X2] :
( ssItem(X2)
=> app(W,cons(X2,nil)) != X )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Z,X1) = U
& app(app(Z,cons(Y,nil)),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| ~ neq(V,nil) ) )
| 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(f219,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(f248,plain,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f249,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f248]) ).
fof(f388,plain,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f84]) ).
fof(f389,plain,
! [X0] :
( ~ ssList(X0)
| X0 = app(X0,nil) ),
inference(cnf_transformation,[status(thm)],[f388]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| ( ? [X2] :
( app(W,cons(X2,nil)) = X
& ssItem(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Z,X1) != U
| app(app(Z,cons(Y,nil)),X1) != V
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& neq(V,nil) ) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [U,V,W,X] :
( sP0_prd(X,W,V,U)
<=> ( ? [X2] :
( app(W,cons(X2,nil)) = X
& ssItem(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Z,X1) != U
| app(app(Z,cons(Y,nil)),X1) != V
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& neq(V,nil) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| sP0_prd(X,W,V,U) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( ~ neq(sK50_skl,nil)
& neq(sK48_skl,nil) )
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,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]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl)],[f417]) ).
fof(f419,plain,
ssList(sK47_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f420,plain,
ssList(sK48_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f423,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f424,plain,
sK49_skl = sK47_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f425,plain,
( neq(sK48_skl,nil)
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
( ~ neq(sK50_skl,nil)
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
! [U,V,W,X] :
( ( ! [X2] :
( app(W,cons(X2,nil)) != X
| ~ ssItem(X2) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Z,X1) = U
& app(app(Z,cons(Y,nil)),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ( ( ? [X2] :
( app(W,cons(X2,nil)) = X
& ssItem(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Z,X1) != U
| app(app(Z,cons(Y,nil)),X1) != V
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f428,plain,
( ! [U,V,W,X] :
( ! [X2] :
( app(W,cons(X2,nil)) != X
| ~ ssItem(X2) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Z,X1) = U
& app(app(Z,cons(Y,nil)),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( ? [X2] :
( app(W,cons(X2,nil)) = X
& ssItem(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Z,X1) != U
| app(app(Z,cons(Y,nil)),X1) != V
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(miniscoping,[status(thm)],[f427]) ).
fof(f429,plain,
( ! [U,V,W,X] :
( ! [X2] :
( app(W,cons(X2,nil)) != X
| ~ ssItem(X2) )
| ( app(sK53_skl(X,W,V,U),sK54_skl(X,W,V,U)) = U
& app(app(sK53_skl(X,W,V,U),cons(sK52_skl(X,W,V,U),nil)),sK54_skl(X,W,V,U)) = V
& ssList(sK54_skl(X,W,V,U))
& ssList(sK53_skl(X,W,V,U))
& ssItem(sK52_skl(X,W,V,U)) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( app(W,cons(sK51_skl(X,W,V,U),nil)) = X
& ssItem(sK51_skl(X,W,V,U))
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Z,X1) != U
| app(app(Z,cons(Y,nil)),X1) != V
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51_skl,sK52_skl,sK53_skl,sK54_skl]),skolemize(X2,sK51_skl(X,W,V,U)),skolemize(Y,sK52_skl(X,W,V,U)),skolemize(Z,sK53_skl(X,W,V,U)),skolemize(X1,sK54_skl(X,W,V,U))],[f428]) ).
fof(f430,plain,
! [X0,X1,X2,X3] :
( neq(X2,nil)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f431,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( app(X5,X6) != X3
| app(app(X5,cons(X4,nil)),X6) != X2
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f432,plain,
! [X0,X1,X2,X3] :
( ~ sP0_prd(X0,X1,X2,X3)
| ssItem(sK51_skl(X0,X1,X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f433,plain,
! [X0,X1,X2,X3] :
( ~ sP0_prd(X1,X0,X2,X3)
| app(X0,cons(sK51_skl(X1,X0,X2,X3),nil)) = X1 ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f439,definition,
( sQ0_spl
<=> sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f440,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f442,definition,
( sQ1_spl
<=> neq(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( ~ sQ1_spl
| neq(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f425,f439,f442]) ).
fof(f446,definition,
( sQ2_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f448,plain,
( sQ2_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f449,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f439,f446]) ).
fof(f451,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X2)
| ~ ssList(app(app(X0,X1),X2))
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f137]) ).
fof(f452,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f453,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f452]) ).
fof(f465,plain,
! [X0,X1,X2,X3,X4] :
( ~ ssList(X3)
| ~ ssList(X4)
| ~ sP0_prd(X1,X2,app(app(X3,cons(X0,nil)),X4),app(X3,X4))
| ~ ssItem(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f431]) ).
fof(f496,plain,
( ~ sQ0_spl
| sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f440]) ).
fof(f497,plain,
( ~ sQ0_spl
| sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f496]) ).
fof(f498,plain,
( ~ sQ0_spl
| app(sK47_skl,cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil)) = sK48_skl ),
inference(resolution,[status(thm)],[f433,f497]) ).
fof(f499,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ ssList(sK47_skl)
| ~ ssList(X2)
| ~ sP0_prd(X0,X1,app(sK48_skl,X2),app(sK47_skl,X2))
| ~ ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl)) ),
inference(paramodulation,[status(thm)],[f498,f465]) ).
fof(f507,definition,
( sQ7_spl
<=> ssList(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f509,plain,
( sQ7_spl
| ~ ssList(sK47_skl) ),
inference(component_clause,[status(thm)],[f507]) ).
fof(f511,definition,
( sQ8_spl
<=> ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f513,plain,
( sQ8_spl
| ~ ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f511]) ).
fof(f514,definition,
! [X0,X1,X2] :
( sQ9_spl
<=> ( ~ ssList(X2)
| ~ sP0_prd(X0,X1,app(sK48_skl,X2),app(sK47_skl,X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f515,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ ssList(X2)
| ~ sP0_prd(X0,X1,app(sK48_skl,X2),app(sK47_skl,X2)) ),
inference(component_clause,[status(thm)],[f514]) ).
fof(f517,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f499,f511,f514,f507,f439]) ).
fof(f518,plain,
( sQ2_spl
| ~ neq(sK48_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f423,f448]) ).
fof(f519,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f509,f419]) ).
fof(f520,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f519]) ).
fof(f522,plain,
( ~ sQ1_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f443,f518]) ).
fof(f523,plain,
( ~ sQ1_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f522]) ).
fof(f525,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X0,X1,nil,X2)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f453,f430]) ).
fof(f526,definition,
( sQ10_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f528,plain,
( sQ10_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f526]) ).
fof(f529,definition,
! [X0,X1,X2] :
( sQ11_spl
<=> ~ sP0_prd(X0,X1,nil,X2) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f532,plain,
( sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f525,f526,f529]) ).
fof(f533,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f528,f223]) ).
fof(f534,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f533]) ).
fof(f549,plain,
sK47_skl = app(nil,sK47_skl),
inference(resolution,[status(thm)],[f249,f419]) ).
fof(f550,plain,
nil = app(nil,nil),
inference(resolution,[status(thm)],[f249,f223]) ).
fof(f551,plain,
app(nil,sK48_skl) = sK48_skl,
inference(resolution,[status(thm)],[f249,f420]) ).
fof(f554,plain,
! [X0,X1,X2] :
( ~ ssList(nil)
| ~ ssList(sK47_skl)
| ~ sP0_prd(X1,X2,app(app(nil,cons(X0,nil)),sK47_skl),sK47_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f549,f465]) ).
fof(f555,definition,
! [X0,X1,X2] :
( sQ13_spl
<=> ( ~ sP0_prd(X1,X2,app(app(nil,cons(X0,nil)),sK47_skl),sK47_skl)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f558,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f554,f555,f507,f526]) ).
fof(f559,plain,
! [X0,X1,X2] :
( ~ ssList(nil)
| ~ ssList(sK48_skl)
| ~ sP0_prd(X1,X2,app(app(nil,cons(X0,nil)),sK48_skl),sK48_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f551,f465]) ).
fof(f560,definition,
! [X0,X1,X2] :
( sQ14_spl
<=> ( ~ sP0_prd(X1,X2,app(app(nil,cons(X0,nil)),sK48_skl),sK48_skl)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f563,definition,
( sQ15_spl
<=> ssList(sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f565,plain,
( sQ15_spl
| ~ ssList(sK48_skl) ),
inference(component_clause,[status(thm)],[f563]) ).
fof(f566,plain,
( ~ sQ10_spl
| ~ sQ15_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f559,f560,f563,f526]) ).
fof(f569,plain,
( sQ8_spl
| ~ sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(resolution,[status(thm)],[f513,f432]) ).
fof(f570,plain,
( sQ8_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f569,f497]) ).
fof(f571,plain,
( sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f570]) ).
fof(f595,plain,
! [X0,X1,X2] :
( ~ ssList(nil)
| ~ ssList(nil)
| ~ sP0_prd(X1,X2,app(app(nil,cons(X0,nil)),nil),nil)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f550,f465]) ).
fof(f596,definition,
! [X0,X1,X2] :
( sQ19_spl
<=> ( ~ sP0_prd(X1,X2,app(app(nil,cons(X0,nil)),nil),nil)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f599,plain,
( ~ sQ10_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f595,f596,f526]) ).
fof(f615,plain,
! [X0] :
( ~ ssList(nil)
| segmentP(app(app(nil,nil),X0),nil)
| ~ ssList(X0)
| ~ ssList(app(nil,X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f550,f451]) ).
fof(f616,plain,
! [X0] :
( ~ ssList(sK48_skl)
| segmentP(app(app(nil,sK48_skl),X0),sK48_skl)
| ~ ssList(X0)
| ~ ssList(app(sK48_skl,X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f551,f451]) ).
fof(f617,plain,
! [X0] :
( ~ ssList(sK47_skl)
| segmentP(app(app(nil,sK47_skl),X0),sK47_skl)
| ~ ssList(X0)
| ~ ssList(app(sK47_skl,X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f549,f451]) ).
fof(f622,definition,
! [X0] :
( sQ23_spl
<=> ( segmentP(app(app(nil,nil),X0),nil)
| ~ ssList(X0)
| ~ ssList(app(nil,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f625,plain,
( sQ23_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f615,f526,f622]) ).
fof(f626,definition,
! [X0] :
( sQ24_spl
<=> ( segmentP(app(app(nil,sK48_skl),X0),sK48_skl)
| ~ ssList(X0)
| ~ ssList(app(sK48_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f629,plain,
( ~ sQ15_spl
| sQ24_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f616,f526,f626,f563]) ).
fof(f630,definition,
! [X0] :
( sQ25_spl
<=> ( segmentP(app(app(nil,sK47_skl),X0),sK47_skl)
| ~ ssList(X0)
| ~ ssList(app(sK47_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f633,plain,
( ~ sQ7_spl
| sQ25_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f617,f526,f630,f507]) ).
fof(f634,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f565,f420]) ).
fof(f635,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f634]) ).
fof(f640,plain,
app(sK47_skl,nil) = sK47_skl,
inference(resolution,[status(thm)],[f389,f419]) ).
fof(f642,plain,
app(sK48_skl,nil) = sK48_skl,
inference(resolution,[status(thm)],[f389,f420]) ).
fof(f644,plain,
! [X0] :
( ~ ssList(nil)
| segmentP(app(app(sK48_skl,nil),X0),nil)
| ~ ssList(X0)
| ~ ssList(app(sK48_skl,X0))
| ~ ssList(sK48_skl) ),
inference(paramodulation,[status(thm)],[f642,f451]) ).
fof(f645,plain,
! [X0,X1,X2] :
( ~ ssList(sK48_skl)
| ~ ssList(nil)
| ~ sP0_prd(X1,X2,app(app(sK48_skl,cons(X0,nil)),nil),sK48_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f642,f465]) ).
fof(f650,definition,
! [X0,X1,X2] :
( sQ27_spl
<=> ( ~ sP0_prd(X1,X2,app(app(sK48_skl,cons(X0,nil)),nil),sK48_skl)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f653,plain,
( ~ sQ15_spl
| ~ sQ10_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f645,f650,f526,f563]) ).
fof(f654,definition,
! [X0] :
( sQ28_spl
<=> ( segmentP(app(app(sK48_skl,nil),X0),nil)
| ~ ssList(X0)
| ~ ssList(app(sK48_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f657,plain,
( ~ sQ10_spl
| sQ28_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f644,f563,f654,f526]) ).
fof(f663,plain,
! [X0,X1] :
( ~ sQ9_spl
| ~ ssList(nil)
| ~ sP0_prd(X0,X1,app(sK48_skl,nil),sK47_skl) ),
inference(paramodulation,[status(thm)],[f640,f515]) ).
fof(f664,plain,
! [X0] :
( ~ ssList(nil)
| segmentP(app(app(sK47_skl,nil),X0),nil)
| ~ ssList(X0)
| ~ ssList(app(sK47_skl,X0))
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f640,f451]) ).
fof(f665,plain,
! [X0,X1,X2] :
( ~ ssList(sK47_skl)
| ~ ssList(nil)
| ~ sP0_prd(X1,X2,app(app(sK47_skl,cons(X0,nil)),nil),sK47_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f640,f465]) ).
fof(f666,definition,
! [X0,X1] :
( sQ29_spl
<=> ~ sP0_prd(X0,X1,app(sK48_skl,nil),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f667,plain,
! [X0,X1] :
( ~ sQ29_spl
| ~ sP0_prd(X0,X1,app(sK48_skl,nil),sK47_skl) ),
inference(component_clause,[status(thm)],[f666]) ).
fof(f669,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f663,f666,f526,f514]) ).
fof(f670,definition,
! [X0] :
( sQ30_spl
<=> ( segmentP(app(app(sK47_skl,nil),X0),nil)
| ~ ssList(X0)
| ~ ssList(app(sK47_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f673,plain,
( ~ sQ10_spl
| sQ30_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f664,f507,f670,f526]) ).
fof(f674,definition,
! [X0,X1,X2] :
( sQ31_spl
<=> ( ~ sP0_prd(X1,X2,app(app(sK47_skl,cons(X0,nil)),nil),sK47_skl)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f677,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f665,f674,f526,f507]) ).
fof(f679,plain,
! [X0,X1] :
( ~ sQ29_spl
| ~ sP0_prd(X0,X1,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f642,f667]) ).
fof(f680,plain,
( ~ sQ0_spl
| ~ sQ29_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f497,f679]) ).
fof(f681,plain,
( ~ sQ0_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f680]) ).
fof(f682,plain,
$false,
inference(sat_refutation,[status(thm)],[f445,f449,f517,f520,f523,f532,f534,f558,f566,f571,f599,f625,f629,f633,f635,f653,f657,f669,f673,f677,f681]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC012+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n005.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 07:48:47 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.48 % Drodi V4.1.1
% 95.10/12.54 % Refutation found
% 95.10/12.54 % SZS status Theorem for theBenchmark: Theorem is valid
% 95.10/12.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.32/12.61 % Elapsed time: 12.154318 seconds
% 5.32/12.61 % CPU time: 95.657080 seconds
% 5.32/12.61 % Total memory used: 377.339 MB
% 5.32/12.61 % Net memory used: 346.912 MB
%------------------------------------------------------------------------------