%------------------------------------------------------------------------------
% 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/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 : Theorem 231.02s 29.74s
% Output : CNFRefutation 134.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 27
% Syntax : Number of formulae : 129 ( 26 unt; 18 def)
% Number of atoms : 500 ( 76 equ)
% Maximal formula atoms : 27 ( 3 avg)
% Number of connectives : 591 ( 220 ~; 222 |; 97 &)
% ( 22 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 19 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 9 con; 0-2 aty)
% Number of variables : 156 ( 116 !; 40 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
? [U] :
( ? [V] :
( U != V
& ssItem(V) )
& ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [U] :
( ssList(U)
=> ( strictorderedP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> lt(V,W) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [U] :
( ssList(U)
=> ( duplicatefreeP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> V != W ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [U] :
( ssItem(U)
=> leq(U,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f90,axiom,
! [U] :
( ssItem(U)
=> ~ lt(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 = W
& nil != X )
| duplicatefreeP(U)
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( lt(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] :
( lt(X1,X3)
& app(cons(X3,nil),X4) = W
& ssList(X4) )
& ssItem(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ strictorderedP(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)
=> ( ( nil = W
& nil != X )
| duplicatefreeP(U)
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( lt(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] :
( lt(X1,X3)
& app(cons(X3,nil),X4) = W
& ssList(X4) )
& ssItem(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ strictorderedP(W)
| app(app(Y,W),Z) != X ) ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f102,plain,
( sK0_skl != sK1_skl
& ssItem(sK1_skl)
& ssItem(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl)],[f2]) ).
fof(f103,plain,
ssItem(sK0_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f104,plain,
ssItem(sK1_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f185,plain,
! [U] :
( ( strictorderedP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( lt(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f186,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( ~ lt(V,W)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| strictorderedP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( lt(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ strictorderedP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f185]) ).
fof(f187,plain,
! [U] :
( ( ( ( ~ lt(sK29_skl(U),sK30_skl(U))
& app(app(sK31_skl(U),cons(sK29_skl(U),sK32_skl(U))),cons(sK30_skl(U),sK33_skl(U))) = U
& ssList(sK33_skl(U))
& ssList(sK32_skl(U))
& ssList(sK31_skl(U))
& ssItem(sK30_skl(U))
& ssItem(sK29_skl(U)) )
| strictorderedP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( lt(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ strictorderedP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29_skl,sK30_skl,sK31_skl,sK32_skl,sK33_skl]),skolemize(V,sK29_skl(U)),skolemize(W,sK30_skl(U)),skolemize(X,sK31_skl(U)),skolemize(Y,sK32_skl(U)),skolemize(Z,sK33_skl(U))],[f186]) ).
fof(f188,plain,
! [X0,X1,X2,X3,X4,X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ strictorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f196,plain,
! [U] :
( ( duplicatefreeP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( V != W
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f197,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( V = W
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| duplicatefreeP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( V != W
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ duplicatefreeP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f196]) ).
fof(f198,plain,
! [U] :
( ( ( ( sK34_skl(U) = sK35_skl(U)
& app(app(sK36_skl(U),cons(sK34_skl(U),sK37_skl(U))),cons(sK35_skl(U),sK38_skl(U))) = U
& ssList(sK38_skl(U))
& ssList(sK37_skl(U))
& ssList(sK36_skl(U))
& ssItem(sK35_skl(U))
& ssItem(sK34_skl(U)) )
| duplicatefreeP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( V != W
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ duplicatefreeP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34_skl,sK35_skl,sK36_skl,sK37_skl,sK38_skl]),skolemize(V,sK34_skl(U)),skolemize(W,sK35_skl(U)),skolemize(X,sK36_skl(U)),skolemize(Y,sK37_skl(U)),skolemize(Z,sK38_skl(U))],[f197]) ).
fof(f200,plain,
! [X0] :
( ssItem(sK34_skl(X0))
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f202,plain,
! [X0] :
( ~ ssList(X0)
| duplicatefreeP(X0)
| ssList(sK36_skl(X0)) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f203,plain,
! [X0] :
( ~ ssList(X0)
| ssList(sK37_skl(X0))
| duplicatefreeP(X0) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f204,plain,
! [X0] :
( ssList(sK38_skl(X0))
| ~ ssList(X0)
| duplicatefreeP(X0) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f205,plain,
! [X0] :
( X0 = app(app(sK36_skl(X0),cons(sK34_skl(X0),sK37_skl(X0))),cons(sK35_skl(X0),sK38_skl(X0)))
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f206,plain,
! [X0] :
( duplicatefreeP(X0)
| ~ ssList(X0)
| sK34_skl(X0) = sK35_skl(X0) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f254,plain,
! [U] :
( leq(U,U)
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f255,plain,
! [X0] :
( ~ ssItem(X0)
| leq(X0,X0) ),
inference(cnf_transformation,[status(thm)],[f254]) ).
fof(f304,plain,
! [U] :
( rearsegP(U,U)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f305,plain,
! [X0] :
( ~ ssList(X0)
| rearsegP(X0,X0) ),
inference(cnf_transformation,[status(thm)],[f304]) ).
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(f400,plain,
! [U] :
( ~ lt(U,U)
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f90]) ).
fof(f401,plain,
! [X0] :
( ~ lt(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f400]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( nil != W
| nil = X )
& ~ duplicatefreeP(U)
& ? [Y] :
( ? [Z] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ lt(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] :
( ~ lt(X1,X3)
| app(cons(X3,nil),X4) != W
| ~ ssList(X4) )
| ~ ssItem(X3) )
| app(X2,cons(X1,nil)) != Y
| ~ ssList(X2) )
| ~ ssItem(X1) )
& strictorderedP(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] :
( ( nil != W
| nil = X )
& ~ duplicatefreeP(U)
& ? [Y] :
( ? [Z] :
( ! [X5] :
( ! [X7] :
( ~ lt(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] :
( ~ lt(X1,X3)
| ! [X4] :
( app(cons(X3,nil),X4) != W
| ~ ssList(X4) )
| ~ ssItem(X3) )
| ! [X2] :
( app(X2,cons(X1,nil)) != Y
| ~ ssList(X2) )
| ~ ssItem(X1) )
& strictorderedP(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,
( ( nil != sK49_skl
| nil = sK50_skl )
& ~ duplicatefreeP(sK47_skl)
& ! [X5] :
( ! [X7] :
( ~ lt(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] :
( ~ lt(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) )
& strictorderedP(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(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(f427,plain,
strictorderedP(sK49_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f430,plain,
~ duplicatefreeP(sK47_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f468,plain,
! [X0,X1,X2,X3,X4] :
( ~ ssList(X4)
| ~ ssList(app(app(X3,cons(X1,X0)),cons(X2,X4)))
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ strictorderedP(app(app(X3,cons(X1,X0)),cons(X2,X4)))
| lt(X1,X2)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f188]) ).
fof(f492,plain,
~ duplicatefreeP(sK49_skl),
inference(backward_demodulation,[status(thm)],[f423,f430]) ).
fof(f562,definition,
( sQ8_spl
<=> lt(sK1_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f563,plain,
( ~ sQ8_spl
| lt(sK1_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f562]) ).
fof(f602,plain,
segmentP(nil,nil),
inference(resolution,[status(thm)],[f319,f223]) ).
fof(f614,plain,
leq(sK1_skl,sK1_skl),
inference(resolution,[status(thm)],[f255,f104]) ).
fof(f615,plain,
leq(sK0_skl,sK0_skl),
inference(resolution,[status(thm)],[f255,f103]) ).
fof(f649,plain,
~ lt(sK1_skl,sK1_skl),
inference(resolution,[status(thm)],[f401,f104]) ).
fof(f705,definition,
( sQ23_spl
<=> ssList(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f707,plain,
( sQ23_spl
| ~ ssList(sK51_skl) ),
inference(component_clause,[status(thm)],[f705]) ).
fof(f725,definition,
( sQ27_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f727,plain,
( sQ27_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f725]) ).
fof(f913,plain,
rearsegP(sK49_skl,sK49_skl),
inference(resolution,[status(thm)],[f305,f420]) ).
fof(f926,plain,
( app(app(sK36_skl(sK49_skl),cons(sK34_skl(sK49_skl),sK37_skl(sK49_skl))),cons(sK35_skl(sK49_skl),sK38_skl(sK49_skl))) = sK49_skl
| duplicatefreeP(sK49_skl) ),
inference(resolution,[status(thm)],[f205,f420]) ).
fof(f931,definition,
( sQ47_spl
<=> duplicatefreeP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f932,plain,
( ~ sQ47_spl
| duplicatefreeP(sK49_skl) ),
inference(component_clause,[status(thm)],[f931]) ).
fof(f934,definition,
( sQ48_spl
<=> app(app(sK36_skl(sK49_skl),cons(sK34_skl(sK49_skl),sK37_skl(sK49_skl))),cons(sK35_skl(sK49_skl),sK38_skl(sK49_skl))) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f935,plain,
( ~ sQ48_spl
| sK49_skl = app(app(sK36_skl(sK49_skl),cons(sK34_skl(sK49_skl),sK37_skl(sK49_skl))),cons(sK35_skl(sK49_skl),sK38_skl(sK49_skl))) ),
inference(component_clause,[status(thm)],[f934]) ).
fof(f937,plain,
( sQ48_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f926,f931,f934]) ).
fof(f966,plain,
( ~ sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f932,f492]) ).
fof(f967,plain,
~ sQ47_spl,
inference(contradiction_clause,[status(thm)],[f966]) ).
fof(f1152,definition,
( sQ65_spl
<=> segmentP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f1154,plain,
( sQ65_spl
| ~ segmentP(nil,nil) ),
inference(component_clause,[status(thm)],[f1152]) ).
fof(f1275,plain,
( sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f727,f420]) ).
fof(f1276,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f1275]) ).
fof(f1313,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f707,f424]) ).
fof(f1314,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f1313]) ).
fof(f1374,definition,
! [X0] :
( sQ82_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1375,plain,
! [X0] :
( ~ sQ82_spl
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1374]) ).
fof(f1381,plain,
! [X0] :
( ~ sQ82_spl
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1375]) ).
fof(f1431,plain,
( ~ sQ82_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f424,f1381]) ).
fof(f1433,plain,
~ sQ82_spl,
inference(contradiction_clause,[status(thm)],[f1431]) ).
fof(f2078,definition,
( sQ138_spl
<=> rearsegP(sK49_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f2080,plain,
( sQ138_spl
| ~ rearsegP(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f2078]) ).
fof(f2082,plain,
( sQ138_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2080,f913]) ).
fof(f2083,plain,
sQ138_spl,
inference(contradiction_clause,[status(thm)],[f2082]) ).
fof(f2218,plain,
( sQ65_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1154,f602]) ).
fof(f2219,plain,
sQ65_spl,
inference(contradiction_clause,[status(thm)],[f2218]) ).
fof(f3300,plain,
( duplicatefreeP(sK49_skl)
| sK34_skl(sK49_skl) = sK35_skl(sK49_skl) ),
inference(resolution,[status(thm)],[f206,f420]) ).
fof(f3330,definition,
( sQ217_spl
<=> sK34_skl(sK49_skl) = sK35_skl(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition]) ).
fof(f3331,plain,
( ~ sQ217_spl
| sK35_skl(sK49_skl) = sK34_skl(sK49_skl) ),
inference(component_clause,[status(thm)],[f3330]) ).
fof(f3333,plain,
( sQ47_spl
| sQ217_spl ),
inference(split_clause,[status(thm)],[f3300,f3330,f931]) ).
fof(f8301,plain,
( ~ sQ217_spl
| ssItem(sK35_skl(sK49_skl))
| ~ ssList(sK49_skl)
| duplicatefreeP(sK49_skl) ),
inference(paramodulation,[status(thm)],[f3331,f200]) ).
fof(f8302,definition,
( sQ413_spl
<=> ssItem(sK35_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ413_spl])],[split_symbol_definition]) ).
fof(f8303,plain,
( ~ sQ413_spl
| ssItem(sK35_skl(sK49_skl)) ),
inference(component_clause,[status(thm)],[f8302]) ).
fof(f8305,plain,
( ~ sQ217_spl
| sQ413_spl
| ~ sQ27_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f8301,f931,f725,f8302,f3330]) ).
fof(f8349,plain,
( ~ sQ413_spl
| ~ lt(sK35_skl(sK49_skl),sK35_skl(sK49_skl)) ),
inference(resolution,[status(thm)],[f8303,f401]) ).
fof(f8359,definition,
( sQ415_spl
<=> lt(sK35_skl(sK49_skl),sK35_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ415_spl])],[split_symbol_definition]) ).
fof(f8360,plain,
( ~ sQ415_spl
| lt(sK35_skl(sK49_skl),sK35_skl(sK49_skl)) ),
inference(component_clause,[status(thm)],[f8359]) ).
fof(f9013,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f563,f649]) ).
fof(f9014,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f9013]) ).
fof(f9521,definition,
( sQ458_spl
<=> leq(sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ458_spl])],[split_symbol_definition]) ).
fof(f9523,plain,
( sQ458_spl
| ~ leq(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f9521]) ).
fof(f9528,definition,
( sQ460_spl
<=> leq(sK1_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ460_spl])],[split_symbol_definition]) ).
fof(f9530,plain,
( sQ460_spl
| ~ leq(sK1_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f9528]) ).
fof(f9553,plain,
( sQ460_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9530,f614]) ).
fof(f9554,plain,
sQ460_spl,
inference(contradiction_clause,[status(thm)],[f9553]) ).
fof(f9563,plain,
( sQ458_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9523,f615]) ).
fof(f9564,plain,
sQ458_spl,
inference(contradiction_clause,[status(thm)],[f9563]) ).
fof(f9631,definition,
( sQ471_spl
<=> ssItem(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ471_spl])],[split_symbol_definition]) ).
fof(f9633,plain,
( sQ471_spl
| ~ ssItem(sK1_skl) ),
inference(component_clause,[status(thm)],[f9631]) ).
fof(f9635,plain,
( sQ471_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9633,f104]) ).
fof(f9636,plain,
sQ471_spl,
inference(contradiction_clause,[status(thm)],[f9635]) ).
fof(f9753,plain,
( ~ sQ48_spl
| ~ sQ217_spl
| app(app(sK36_skl(sK49_skl),cons(sK35_skl(sK49_skl),sK37_skl(sK49_skl))),cons(sK35_skl(sK49_skl),sK38_skl(sK49_skl))) = sK49_skl ),
inference(forward_demodulation,[status(thm)],[f3331,f935]) ).
fof(f9792,definition,
( sQ486_spl
<=> ssList(sK36_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ486_spl])],[split_symbol_definition]) ).
fof(f9794,plain,
( sQ486_spl
| ~ ssList(sK36_skl(sK49_skl)) ),
inference(component_clause,[status(thm)],[f9792]) ).
fof(f9804,plain,
( sQ486_spl
| ~ ssList(sK49_skl)
| duplicatefreeP(sK49_skl) ),
inference(resolution,[status(thm)],[f9794,f202]) ).
fof(f9805,plain,
( sQ486_spl
| ~ sQ27_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f9804,f931,f725,f9792]) ).
fof(f9942,plain,
( ~ sQ48_spl
| ~ sQ217_spl
| ~ ssList(sK38_skl(sK49_skl))
| ~ ssList(sK49_skl)
| ~ ssItem(sK35_skl(sK49_skl))
| ~ ssItem(sK35_skl(sK49_skl))
| ~ ssList(sK36_skl(sK49_skl))
| ~ strictorderedP(app(app(sK36_skl(sK49_skl),cons(sK35_skl(sK49_skl),sK37_skl(sK49_skl))),cons(sK35_skl(sK49_skl),sK38_skl(sK49_skl))))
| lt(sK35_skl(sK49_skl),sK35_skl(sK49_skl))
| ~ ssList(sK37_skl(sK49_skl)) ),
inference(paramodulation,[status(thm)],[f9753,f468]) ).
fof(f9944,definition,
( sQ510_spl
<=> ssList(sK38_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ510_spl])],[split_symbol_definition]) ).
fof(f9946,plain,
( sQ510_spl
| ~ ssList(sK38_skl(sK49_skl)) ),
inference(component_clause,[status(thm)],[f9944]) ).
fof(f9951,definition,
( sQ512_spl
<=> ssList(sK37_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ512_spl])],[split_symbol_definition]) ).
fof(f9953,plain,
( sQ512_spl
| ~ ssList(sK37_skl(sK49_skl)) ),
inference(component_clause,[status(thm)],[f9951]) ).
fof(f9954,definition,
( sQ513_spl
<=> strictorderedP(app(app(sK36_skl(sK49_skl),cons(sK35_skl(sK49_skl),sK37_skl(sK49_skl))),cons(sK35_skl(sK49_skl),sK38_skl(sK49_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ513_spl])],[split_symbol_definition]) ).
fof(f9956,plain,
( sQ513_spl
| ~ strictorderedP(app(app(sK36_skl(sK49_skl),cons(sK35_skl(sK49_skl),sK37_skl(sK49_skl))),cons(sK35_skl(sK49_skl),sK38_skl(sK49_skl)))) ),
inference(component_clause,[status(thm)],[f9954]) ).
fof(f9957,plain,
( ~ sQ48_spl
| ~ sQ217_spl
| ~ sQ510_spl
| ~ sQ27_spl
| ~ sQ413_spl
| ~ sQ486_spl
| ~ sQ513_spl
| sQ415_spl
| ~ sQ512_spl ),
inference(split_clause,[status(thm)],[f9942,f9951,f8359,f9954,f9792,f8302,f725,f9944,f3330,f934]) ).
fof(f9959,plain,
( sQ513_spl
| ~ sQ48_spl
| ~ sQ217_spl
| ~ strictorderedP(sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f9753,f9956]) ).
fof(f9960,plain,
( sQ513_spl
| ~ sQ48_spl
| ~ sQ217_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9959,f427]) ).
fof(f9961,plain,
( sQ513_spl
| ~ sQ48_spl
| ~ sQ217_spl ),
inference(contradiction_clause,[status(thm)],[f9960]) ).
fof(f10042,plain,
( sQ512_spl
| ~ ssList(sK49_skl)
| duplicatefreeP(sK49_skl) ),
inference(resolution,[status(thm)],[f9953,f203]) ).
fof(f10043,plain,
( sQ512_spl
| ~ sQ27_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f10042,f931,f725,f9951]) ).
fof(f10044,plain,
( ~ sQ415_spl
| ~ sQ413_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8360,f8349]) ).
fof(f10045,plain,
( ~ sQ415_spl
| ~ sQ413_spl ),
inference(contradiction_clause,[status(thm)],[f10044]) ).
fof(f10046,plain,
( sQ510_spl
| ~ ssList(sK49_skl)
| duplicatefreeP(sK49_skl) ),
inference(resolution,[status(thm)],[f9946,f204]) ).
fof(f10047,plain,
( sQ510_spl
| ~ sQ27_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f10046,f931,f725,f9944]) ).
fof(f10048,plain,
$false,
inference(sat_refutation,[status(thm)],[f937,f967,f1276,f1314,f1433,f2083,f2219,f3333,f8305,f9014,f9554,f9564,f9636,f9805,f9957,f9961,f10043,f10045,f10047]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p
% 0.15/0.39 % Computer : n010.cluster.edu
% 0.15/0.39 % Model : x86_64 x86_64
% 0.15/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.39 % Memory : 8046.5625MB
% 0.15/0.39 % OS : Linux 6.8.0-71-generic
% 0.15/0.39 % CPULimit : 300
% 0.15/0.39 % WCLimit : 300
% 0.15/0.39 % DateTime : Mon Sep 21 08:02:24 UTC 2026
% 0.15/0.39 % CPUTime :
% 0.19/0.44 % Drodi V4.1.1
% 231.02/29.74 % Refutation found
% 231.02/29.74 % SZS status Theorem for theBenchmark: Theorem is valid
% 231.02/29.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 57.08/29.82 % Elapsed time: 29.406130 seconds
% 57.08/29.82 % CPU time: 232.025473 seconds
% 57.08/29.82 % Total memory used: 441.466 MB
% 57.08/29.82 % Net memory used: 411.513 MB
%------------------------------------------------------------------------------