%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC259+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 02:40:33 PM UTC 2026
% Result : Theorem 0.18s 0.51s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 67 ( 10 unt; 10 def)
% Number of atoms : 295 ( 62 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 353 ( 125 ~; 116 |; 85 &)
% ( 13 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 9 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-5 aty)
% Number of variables : 109 ( 78 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,axiom,
! [U] :
( ssItem(U)
=> totalorderedP(cons(U,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ? [X3] :
( lt(X3,Y)
& memberP(X1,X3)
& ssItem(X3) )
| ? [X2] :
( lt(Y,X2)
& memberP(Z,X2)
& ssItem(X2) )
| app(app(Z,W),X1) != X
| cons(Y,nil) != W
| ~ ssList(X1) ) ) ) )
| totalorderedP(U)
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ? [X3] :
( lt(X3,Y)
& memberP(X1,X3)
& ssItem(X3) )
| ? [X2] :
( lt(Y,X2)
& memberP(Z,X2)
& ssItem(X2) )
| app(app(Z,W),X1) != X
| cons(Y,nil) != W
| ~ ssList(X1) ) ) ) )
| totalorderedP(U)
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f113,plain,
! [U] :
( ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f114,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ? [V] :
( cons(V,nil) = U
& ssItem(V) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ( cons(sK4_skl(U),nil) = U
& ssItem(sK4_skl(U)) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114]) ).
fof(f117,plain,
! [X0] :
( cons(sK4_skl(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f224,plain,
! [U] :
( ! [V] :
( cons(V,U) != U
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f225,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f224]) ).
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] :
( ( ( nil = W
& nil = X )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& ! [X2] :
( ~ lt(Y,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) )
& app(app(Z,W),X1) = X
& cons(Y,nil) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) ) )
& ~ totalorderedP(U)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [W,X,Y] :
( sP0_prd(Y,X,W)
<=> ( ? [Z] :
( ? [X1] :
( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& ! [X2] :
( ~ lt(Y,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) )
& app(app(Z,W),X1) = X
& cons(Y,nil) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [Y] : sP0_prd(Y,X,W) )
& ~ totalorderedP(U)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( nil = sK49_skl
& nil = sK50_skl )
| sP0_prd(sK51_skl,sK50_skl,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)],[f417]) ).
fof(f424,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f425,plain,
~ totalorderedP(sK47_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
( nil = sK50_skl
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
( nil = sK49_skl
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f428,definition,
! [Y,Z,X2] :
( sP1_prd(X2,Z,Y)
<=> ( ~ lt(Y,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f429,plain,
! [W,X,Y] :
( sP0_prd(Y,X,W)
<=> ( ? [Z] :
( ? [X1] :
( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& ! [X2] : sP1_prd(X2,Z,Y)
& app(app(Z,W),X1) = X
& cons(Y,nil) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) ) ),
inference(formula_renaming,[status(thm)],[f416,f428]) ).
fof(f430,plain,
! [W,X,Y] :
( ( ! [Z] :
( ! [X1] :
( ? [X3] :
( lt(X3,Y)
& memberP(X1,X3)
& ssItem(X3) )
| ? [X2] : ~ sP1_prd(X2,Z,Y)
| app(app(Z,W),X1) != X
| cons(Y,nil) != W
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y)
| sP0_prd(Y,X,W) )
& ( ( ? [Z] :
( ? [X1] :
( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& ! [X2] : sP1_prd(X2,Z,Y)
& app(app(Z,W),X1) = X
& cons(Y,nil) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| ~ sP0_prd(Y,X,W) ) ),
inference(NNF_transformation,[status(thm)],[f429]) ).
fof(f431,plain,
( ! [W,X,Y] :
( ! [Z] :
( ! [X1] :
( ? [X3] :
( lt(X3,Y)
& memberP(X1,X3)
& ssItem(X3) )
| ? [X2] : ~ sP1_prd(X2,Z,Y)
| app(app(Z,W),X1) != X
| cons(Y,nil) != W
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y)
| sP0_prd(Y,X,W) )
& ! [W,X,Y] :
( ( ? [Z] :
( ? [X1] :
( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& ! [X2] : sP1_prd(X2,Z,Y)
& app(app(Z,W),X1) = X
& cons(Y,nil) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| ~ sP0_prd(Y,X,W) ) ),
inference(miniscoping,[status(thm)],[f430]) ).
fof(f432,plain,
( ! [W,X,Y] :
( ! [Z] :
( ! [X1] :
( ( lt(sK55_skl(X1,Z,Y,X,W),Y)
& memberP(X1,sK55_skl(X1,Z,Y,X,W))
& ssItem(sK55_skl(X1,Z,Y,X,W)) )
| ~ sP1_prd(sK54_skl(X1,Z,Y,X,W),Z,Y)
| app(app(Z,W),X1) != X
| cons(Y,nil) != W
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y)
| sP0_prd(Y,X,W) )
& ! [W,X,Y] :
( ( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(sK53_skl(Y,X,W),X3)
| ~ ssItem(X3) )
& ! [X2] : sP1_prd(X2,sK52_skl(Y,X,W),Y)
& app(app(sK52_skl(Y,X,W),W),sK53_skl(Y,X,W)) = X
& cons(Y,nil) = W
& ssList(sK53_skl(Y,X,W))
& ssList(sK52_skl(Y,X,W))
& ssItem(Y) )
| ~ sP0_prd(Y,X,W) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52_skl,sK53_skl,sK54_skl,sK55_skl]),skolemize(Z,sK52_skl(Y,X,W)),skolemize(X1,sK53_skl(Y,X,W)),skolemize(X2,sK54_skl(X1,Z,Y,X,W)),skolemize(X3,sK55_skl(X1,Z,Y,X,W))],[f431]) ).
fof(f433,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f432]) ).
fof(f436,plain,
! [X0,X1,X2] :
( cons(X0,nil) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f432]) ).
fof(f449,definition,
( sQ0_spl
<=> sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f450,plain,
( ~ sQ0_spl
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f452,definition,
( sQ1_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f453,plain,
( ~ sQ1_spl
| nil = sK50_skl ),
inference(component_clause,[status(thm)],[f452]) ).
fof(f455,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f449,f452]) ).
fof(f456,definition,
( sQ2_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( ~ sQ2_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f456]) ).
fof(f459,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f427,f449,f456]) ).
fof(f495,plain,
~ totalorderedP(sK49_skl),
inference(forward_demodulation,[status(thm)],[f424,f425]) ).
fof(f496,plain,
( ~ sQ0_spl
| ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f450,f433]) ).
fof(f499,plain,
( ~ sQ0_spl
| cons(sK51_skl,nil) = sK49_skl ),
inference(resolution,[status(thm)],[f436,f450]) ).
fof(f506,definition,
( sQ4_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f508,plain,
( sQ4_spl
| ~ ssItem(sK51_skl) ),
inference(component_clause,[status(thm)],[f506]) ).
fof(f509,definition,
( sQ5_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f511,plain,
( sQ5_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f509]) ).
fof(f521,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f511,f223]) ).
fof(f522,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f521]) ).
fof(f523,plain,
( sQ4_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f508,f496]) ).
fof(f524,plain,
( sQ4_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f523]) ).
fof(f534,plain,
( ~ sQ1_spl
| totalorderedP(sK50_skl) ),
inference(backward_demodulation,[status(thm)],[f453,f339]) ).
fof(f536,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ totalorderedP(sK50_skl) ),
inference(backward_demodulation,[status(thm)],[f539,f495]) ).
fof(f539,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sK50_skl = sK49_skl ),
inference(forward_demodulation,[status(thm)],[f453,f457]) ).
fof(f540,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f536,f534]) ).
fof(f541,plain,
( ~ sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f540]) ).
fof(f542,plain,
( ~ ssItem(sK4_skl(nil))
| ~ ssList(nil)
| ~ singletonP(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f117,f225]) ).
fof(f543,definition,
( sQ8_spl
<=> singletonP(nil) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f546,definition,
( sQ9_spl
<=> ssItem(sK4_skl(nil)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f549,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f542,f509,f543,f546]) ).
fof(f565,plain,
( ~ sQ0_spl
| totalorderedP(sK49_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f499,f338]) ).
fof(f566,definition,
( sQ11_spl
<=> totalorderedP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f567,plain,
( ~ sQ11_spl
| totalorderedP(sK49_skl) ),
inference(component_clause,[status(thm)],[f566]) ).
fof(f569,plain,
( ~ sQ0_spl
| sQ11_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f565,f506,f566,f449]) ).
fof(f570,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f567,f495]) ).
fof(f571,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f570]) ).
fof(f572,plain,
$false,
inference(sat_refutation,[status(thm)],[f455,f459,f522,f524,f541,f549,f569,f571]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC259+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 : n003.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 08:10:30 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.49 % Drodi V4.1.1
% 0.18/0.51 % Refutation found
% 0.18/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.26/0.58 % Elapsed time: 0.127944 seconds
% 0.26/0.58 % CPU time: 0.130954 seconds
% 0.26/0.58 % Total memory used: 14.142 MB
% 0.26/0.58 % Net memory used: 14.124 MB
%------------------------------------------------------------------------------