%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC043+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 : n007.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 02:39:43 PM UTC 2026
% Result : Theorem 0.08s 0.37s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 62 ( 17 unt; 6 def)
% Number of atoms : 234 ( 89 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 276 ( 104 ~; 97 |; 54 &)
% ( 8 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 57 ( 39 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f83,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil = app(U,V)
<=> ( nil = U
& nil = V ) ) ) ),
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)
=> ( ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( lt(X2,Z)
& app(X3,cons(X2,nil)) = W
& ssList(X3) )
& ssItem(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ strictorderedP(W)
| app(W,Y) != X ) )
| nil = U
| U != W
| V != X
| nil != V ) ) ) ) ),
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 )
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( lt(X2,Z)
& app(X3,cons(X2,nil)) = W
& ssList(X3) )
& ssItem(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ strictorderedP(W)
| app(W,Y) != X ) )
| nil = U
| U != W
| V != X
| nil != V ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f383,plain,
! [U] :
( ! [V] :
( ( nil = app(U,V)
<=> ( nil = U
& nil = V ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f83]) ).
fof(f384,plain,
! [U] :
( ! [V] :
( ( ( nil != U
| nil != V
| nil = app(U,V) )
& ( ( nil = U
& nil = V )
| nil != app(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f383]) ).
fof(f385,plain,
! [X0,X1] :
( nil = X1
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f388,plain,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f84]) ).
fof(f389,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f388]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( nil != W
| nil = X )
& ? [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ~ lt(X2,Z)
| app(X3,cons(X2,nil)) != W
| ~ ssList(X3) )
| ~ ssItem(X2) )
| app(cons(Z,nil),X1) != Y
| ~ ssList(X1) )
| ~ ssItem(Z) )
& strictorderedP(W)
& app(W,Y) = X
& ssList(Y) )
& nil != U
& U = W
& V = X
& nil = V
& 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 )
& ? [Y] :
( ! [Z] :
( ! [X2] :
( ~ lt(X2,Z)
| ! [X3] :
( app(X3,cons(X2,nil)) != W
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ! [X1] :
( app(cons(Z,nil),X1) != Y
| ~ ssList(X1) )
| ~ ssItem(Z) )
& strictorderedP(W)
& app(W,Y) = X
& ssList(Y) )
& nil != U
& U = W
& V = X
& nil = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(miniscoping,[status(thm)],[f415]) ).
fof(f417,plain,
( ( nil != sK49_skl
| nil = sK50_skl )
& ! [Z] :
( ! [X2] :
( ~ lt(X2,Z)
| ! [X3] :
( app(X3,cons(X2,nil)) != sK49_skl
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ! [X1] :
( app(cons(Z,nil),X1) != sK51_skl
| ~ ssList(X1) )
| ~ ssItem(Z) )
& strictorderedP(sK49_skl)
& app(sK49_skl,sK51_skl) = sK50_skl
& ssList(sK51_skl)
& nil != sK47_skl
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& nil = sK48_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)],[f416]) ).
fof(f420,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f422,plain,
nil = sK48_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f423,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f424,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f425,plain,
nil != sK47_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f426,plain,
ssList(sK51_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f427,plain,
app(sK49_skl,sK51_skl) = sK50_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f431,definition,
( sQ0_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f432,plain,
( ~ sQ0_spl
| nil = sK50_skl ),
inference(component_clause,[status(thm)],[f431]) ).
fof(f433,plain,
( sQ0_spl
| nil != sK50_skl ),
inference(component_clause,[status(thm)],[f431]) ).
fof(f468,plain,
nil = sK50_skl,
inference(backward_demodulation,[status(thm)],[f423,f422]) ).
fof(f471,plain,
nil != sK49_skl,
inference(forward_demodulation,[status(thm)],[f424,f425]) ).
fof(f472,plain,
( ~ sQ0_spl
| sK50_skl != sK49_skl ),
inference(backward_demodulation,[status(thm)],[f432,f471]) ).
fof(f487,plain,
! [X0] :
( ~ sQ0_spl
| app(X0,sK50_skl) = X0
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f432,f389]) ).
fof(f493,definition,
( sQ2_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f495,plain,
( sQ2_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f493]) ).
fof(f496,definition,
( sQ3_spl
<=> ssList(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f498,plain,
( sQ3_spl
| ~ ssList(sK51_skl) ),
inference(component_clause,[status(thm)],[f496]) ).
fof(f509,plain,
! [X0,X1] :
( ~ sQ0_spl
| nil = X1
| sK50_skl != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f432,f385]) ).
fof(f510,plain,
! [X0,X1] :
( ~ sQ0_spl
| sK50_skl = X1
| sK50_skl != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f432,f509]) ).
fof(f512,plain,
( ~ sQ0_spl
| sK50_skl = sK51_skl
| ~ ssList(sK51_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f510,f427]) ).
fof(f519,definition,
( sQ6_spl
<=> sK50_skl = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f520,plain,
( ~ sQ6_spl
| sK50_skl = sK51_skl ),
inference(component_clause,[status(thm)],[f519]) ).
fof(f522,plain,
( ~ sQ0_spl
| sQ6_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f512,f493,f496,f519,f431]) ).
fof(f525,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f498,f426]) ).
fof(f526,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f525]) ).
fof(f527,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f495,f420]) ).
fof(f528,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f527]) ).
fof(f532,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| app(X0,sK51_skl) = X0
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f520,f487]) ).
fof(f535,plain,
( ~ sQ6_spl
| app(sK49_skl,sK51_skl) = sK51_skl ),
inference(backward_demodulation,[status(thm)],[f520,f427]) ).
fof(f544,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| sK51_skl != sK49_skl ),
inference(backward_demodulation,[status(thm)],[f520,f472]) ).
fof(f570,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| sK51_skl = sK49_skl
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f535,f532]) ).
fof(f571,definition,
( sQ11_spl
<=> sK51_skl = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f572,plain,
( ~ sQ11_spl
| sK51_skl = sK49_skl ),
inference(component_clause,[status(thm)],[f571]) ).
fof(f574,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| sQ11_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f570,f493,f571,f431,f519]) ).
fof(f578,definition,
( sQ13_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f580,plain,
( sQ13_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f578]) ).
fof(f591,plain,
ssList(sK50_skl),
inference(forward_demodulation,[status(thm)],[f468,f223]) ).
fof(f592,plain,
( sQ0_spl
| sK50_skl != sK50_skl ),
inference(forward_demodulation,[status(thm)],[f468,f433]) ).
fof(f593,plain,
( sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f592]) ).
fof(f594,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f593]) ).
fof(f596,plain,
( sQ13_spl
| ~ ssList(sK50_skl) ),
inference(forward_demodulation,[status(thm)],[f468,f580]) ).
fof(f597,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f596,f591]) ).
fof(f598,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f597]) ).
fof(f616,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ11_spl
| sK51_skl != sK51_skl ),
inference(forward_demodulation,[status(thm)],[f572,f544]) ).
fof(f617,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f616]) ).
fof(f618,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f617]) ).
fof(f619,plain,
$false,
inference(sat_refutation,[status(thm)],[f522,f526,f528,f574,f594,f598,f618]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC043+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 07:48:52 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.37 % Refutation found
% 0.08/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.051715 seconds
% 0.13/0.41 % CPU time: 0.111526 seconds
% 0.13/0.41 % Total memory used: 24.545 MB
% 0.13/0.41 % Net memory used: 24.498 MB
%------------------------------------------------------------------------------