%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC287+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 : 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 02:40:39 PM UTC 2026
% Result : Theorem 0.11s 10.64s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 8 unt; 5 def)
% Number of atoms : 183 ( 46 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 218 ( 76 ~; 71 |; 59 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 5 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-3 aty)
% Number of variables : 56 ( 42 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
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(Z,Y)
& 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(Z,Y)
& 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(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(Z,Y)
| ~ 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(Z,Y)
| ~ 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(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(Z,Y)
& memberP(X,Z)
& Y != Z
& ssItem(Z) )
| ~ memberP(X,Y)
| cons(Y,nil) != W
| ~ ssItem(Y)
| sP0_prd(Y,X,W) )
& ( ( ! [Z] :
( ~ leq(Z,Y)
| ~ 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(Z,Y)
& 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(Z,Y)
| ~ 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(sK52_skl(Y,X,W),Y)
& 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(Z,Y)
| ~ 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(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(f496,plain,
( ~ sQ0_spl
| cons(sK51_skl,nil) = sK49_skl ),
inference(resolution,[status(thm)],[f432,f440]) ).
fof(f503,definition,
( sQ4_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f505,plain,
( sQ4_spl
| ~ ssItem(sK51_skl) ),
inference(component_clause,[status(thm)],[f503]) ).
fof(f520,plain,
( sQ4_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f505,f487]) ).
fof(f521,plain,
( sQ4_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f520]) ).
fof(f524,plain,
( ~ sQ2_spl
| ~ strictorderedP(nil) ),
inference(backward_demodulation,[status(thm)],[f447,f486]) ).
fof(f527,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f524,f349]) ).
fof(f528,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f527]) ).
fof(f639,plain,
( ~ sQ0_spl
| strictorderedP(sK49_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f496,f348]) ).
fof(f640,definition,
( sQ19_spl
<=> strictorderedP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f641,plain,
( ~ sQ19_spl
| strictorderedP(sK49_skl) ),
inference(component_clause,[status(thm)],[f640]) ).
fof(f643,plain,
( ~ sQ0_spl
| sQ19_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f639,f503,f640,f439]) ).
fof(f644,plain,
( ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f641,f486]) ).
fof(f645,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f644]) ).
fof(f646,plain,
$false,
inference(sat_refutation,[status(thm)],[f449,f521,f528,f643,f645]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC287+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/10.60 % Computer : n010.cluster.edu
% 0.11/10.60 % Model : x86_64 x86_64
% 0.11/10.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.60 % Memory : 8046.5625MB
% 0.11/10.60 % OS : Linux 6.8.0-71-generic
% 0.11/10.60 % CPULimit : 300
% 0.11/10.60 % WCLimit : 300
% 0.11/10.60 % DateTime : Mon Sep 21 08:13:12 UTC 2026
% 0.11/10.60 % CPUTime :
% 0.11/10.62 % Drodi V4.1.1
% 0.11/10.64 % Refutation found
% 0.11/10.64 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/10.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/10.66 % Elapsed time: 0.055556 seconds
% 0.11/10.66 % CPU time: 0.158026 seconds
% 0.11/10.66 % Total memory used: 86.636 MB
% 0.11/10.66 % Net memory used: 86.522 MB
%------------------------------------------------------------------------------