%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC286+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 02:40:38 PM UTC 2026
% Result : Theorem 0.19s 0.52s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 65 ( 10 unt; 9 def)
% Number of atoms : 253 ( 60 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 297 ( 109 ~; 102 |; 65 &)
% ( 11 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 9 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 72 ( 55 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f68,axiom,
! [U] :
( ssItem(U)
=> strictorderedP(cons(U,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( nil != W
| nil != X )
& ! [Y] :
( ? [Z] :
( leq(Y,Z)
& memberP(X,Z)
& Y != Z
& ssItem(Z) )
| ~ memberP(X,Y)
| cons(Y,nil) != W
| ~ ssItem(Y) ) )
| strictorderedP(U)
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( nil != W
| nil != X )
& ! [Y] :
( ? [Z] :
( leq(Y,Z)
& memberP(X,Z)
& Y != Z
& ssItem(Z) )
| ~ memberP(X,Y)
| cons(Y,nil) != W
| ~ ssItem(Y) ) )
| strictorderedP(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(f347,plain,
! [U] :
( strictorderedP(cons(U,nil))
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f68]) ).
fof(f348,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f347]) ).
fof(f349,plain,
strictorderedP(nil),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [Y] :
( ! [Z] :
( ~ leq(Y,Z)
| ~ memberP(X,Z)
| Y = Z
| ~ ssItem(Z) )
& memberP(X,Y)
& cons(Y,nil) = W
& ssItem(Y) ) )
& ~ strictorderedP(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] :
( ~ leq(Y,Z)
| ~ memberP(X,Z)
| Y = Z
| ~ ssItem(Z) )
& memberP(X,Y)
& cons(Y,nil) = W
& 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) )
& ~ strictorderedP(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) )
& ~ strictorderedP(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,
~ strictorderedP(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,plain,
! [W,X,Y] :
( ( ? [Z] :
( leq(Y,Z)
& memberP(X,Z)
& Y != Z
& ssItem(Z) )
| ~ memberP(X,Y)
| cons(Y,nil) != W
| ~ ssItem(Y)
| sP0_prd(Y,X,W) )
& ( ( ! [Z] :
( ~ leq(Y,Z)
| ~ memberP(X,Z)
| Y = Z
| ~ ssItem(Z) )
& memberP(X,Y)
& cons(Y,nil) = W
& ssItem(Y) )
| ~ sP0_prd(Y,X,W) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f429,plain,
( ! [W,X,Y] :
( ? [Z] :
( leq(Y,Z)
& memberP(X,Z)
& Y != Z
& ssItem(Z) )
| ~ memberP(X,Y)
| cons(Y,nil) != W
| ~ ssItem(Y)
| sP0_prd(Y,X,W) )
& ! [W,X,Y] :
( ( ! [Z] :
( ~ leq(Y,Z)
| ~ memberP(X,Z)
| Y = Z
| ~ ssItem(Z) )
& memberP(X,Y)
& cons(Y,nil) = W
& ssItem(Y) )
| ~ sP0_prd(Y,X,W) ) ),
inference(miniscoping,[status(thm)],[f428]) ).
fof(f430,plain,
( ! [W,X,Y] :
( ( leq(Y,sK52_skl(Y,X,W))
& memberP(X,sK52_skl(Y,X,W))
& Y != sK52_skl(Y,X,W)
& ssItem(sK52_skl(Y,X,W)) )
| ~ memberP(X,Y)
| cons(Y,nil) != W
| ~ ssItem(Y)
| sP0_prd(Y,X,W) )
& ! [W,X,Y] :
( ( ! [Z] :
( ~ leq(Y,Z)
| ~ memberP(X,Z)
| Y = Z
| ~ ssItem(Z) )
& memberP(X,Y)
& cons(Y,nil) = W
& ssItem(Y) )
| ~ sP0_prd(Y,X,W) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52_skl]),skolemize(Z,sK52_skl(Y,X,W))],[f429]) ).
fof(f431,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f430]) ).
fof(f432,plain,
! [X0,X1,X2] :
( cons(X0,nil) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f430]) ).
fof(f439,definition,
( sQ0_spl
<=> sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f440,plain,
( ~ sQ0_spl
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f442,definition,
( sQ1_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( ~ sQ1_spl
| nil = sK50_skl ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f439,f442]) ).
fof(f446,definition,
( sQ2_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f447,plain,
( ~ sQ2_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f449,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f427,f439,f446]) ).
fof(f486,plain,
~ strictorderedP(sK49_skl),
inference(forward_demodulation,[status(thm)],[f424,f425]) ).
fof(f487,plain,
( ~ sQ0_spl
| ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f440,f431]) ).
fof(f491,plain,
( ~ sQ0_spl
| cons(sK51_skl,nil) = sK49_skl ),
inference(resolution,[status(thm)],[f432,f440]) ).
fof(f498,definition,
( sQ4_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f500,plain,
( sQ4_spl
| ~ ssItem(sK51_skl) ),
inference(component_clause,[status(thm)],[f498]) ).
fof(f501,definition,
( sQ5_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f503,plain,
( sQ5_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f501]) ).
fof(f513,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f503,f223]) ).
fof(f514,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f513]) ).
fof(f515,plain,
( sQ4_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f500,f487]) ).
fof(f516,plain,
( sQ4_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f515]) ).
fof(f526,plain,
( ~ sQ1_spl
| strictorderedP(sK50_skl) ),
inference(backward_demodulation,[status(thm)],[f443,f349]) ).
fof(f528,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ strictorderedP(sK50_skl) ),
inference(backward_demodulation,[status(thm)],[f531,f486]) ).
fof(f531,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sK50_skl = sK49_skl ),
inference(forward_demodulation,[status(thm)],[f443,f447]) ).
fof(f532,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f528,f526]) ).
fof(f533,plain,
( ~ sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f532]) ).
fof(f534,plain,
( ~ ssItem(sK4_skl(nil))
| ~ ssList(nil)
| ~ singletonP(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f117,f225]) ).
fof(f535,definition,
( sQ8_spl
<=> singletonP(nil) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f538,definition,
( sQ9_spl
<=> ssItem(sK4_skl(nil)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f541,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f534,f501,f535,f538]) ).
fof(f573,plain,
( ~ sQ0_spl
| strictorderedP(sK49_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f491,f348]) ).
fof(f574,definition,
( sQ14_spl
<=> strictorderedP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f575,plain,
( ~ sQ14_spl
| strictorderedP(sK49_skl) ),
inference(component_clause,[status(thm)],[f574]) ).
fof(f577,plain,
( ~ sQ0_spl
| sQ14_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f573,f498,f574,f439]) ).
fof(f578,plain,
( ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f575,f486]) ).
fof(f579,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f578]) ).
fof(f580,plain,
$false,
inference(sat_refutation,[status(thm)],[f445,f449,f514,f516,f533,f541,f577,f579]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC286+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n018.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Mon Sep 21 08:14:14 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.51 % Drodi V4.1.1
% 0.19/0.52 % Refutation found
% 0.19/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.60 % Elapsed time: 0.124613 seconds
% 0.23/0.60 % CPU time: 0.120914 seconds
% 0.23/0.60 % Total memory used: 6.976 MB
% 0.23/0.60 % Net memory used: 6.968 MB
%------------------------------------------------------------------------------