%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC104+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 : n012.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 02:39:58 PM UTC 2026
% Result : Theorem 0.04s 0.50s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 75 ( 16 unt; 10 def)
% Number of atoms : 274 ( 57 equ)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 316 ( 117 ~; 112 |; 59 &)
% ( 14 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 11 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 70 ( 49 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( frontsegP(V,U)
& neq(U,nil) )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( leq(X2,Z)
& app(X3,cons(X2,nil)) = W
& ssList(X3) )
& ssItem(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ totalorderedP(W)
| app(W,Y) != X ) )
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( frontsegP(V,U)
& neq(U,nil) )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( leq(X2,Z)
& app(X3,cons(X2,nil)) = W
& ssList(X3) )
& ssItem(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ totalorderedP(W)
| app(W,Y) != X ) )
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f119,plain,
! [U] :
( ! [V] :
( ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f120,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ? [W] :
( app(V,W) = U
& ssList(W) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ( app(V,sK5_skl(V,U)) = U
& ssList(sK5_skl(V,U)) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W,sK5_skl(V,U))],[f120]) ).
fof(f124,plain,
! [X0,X1,X2] :
( app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f217,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f218,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f217]) ).
fof(f219,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f220,plain,
! [X0,X1] :
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ frontsegP(V,U)
| ~ neq(U,nil) )
& ( nil != W
| nil = X )
& ? [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ~ leq(X2,Z)
| app(X3,cons(X2,nil)) != W
| ~ ssList(X3) )
| ~ ssItem(X2) )
| app(cons(Z,nil),X1) != Y
| ~ ssList(X1) )
| ~ ssItem(Z) )
& totalorderedP(W)
& app(W,Y) = X
& ssList(Y) )
& neq(V,nil)
& 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] :
( ( ~ frontsegP(V,U)
| ~ neq(U,nil) )
& ( nil != W
| nil = X )
& ? [Y] :
( ! [Z] :
( ! [X2] :
( ~ leq(X2,Z)
| ! [X3] :
( app(X3,cons(X2,nil)) != W
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ! [X1] :
( app(cons(Z,nil),X1) != Y
| ~ ssList(X1) )
| ~ ssItem(Z) )
& totalorderedP(W)
& app(W,Y) = X
& ssList(Y) )
& neq(V,nil)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(miniscoping,[status(thm)],[f415]) ).
fof(f417,plain,
( ( ~ frontsegP(sK48_skl,sK47_skl)
| ~ neq(sK47_skl,nil) )
& ( nil != sK49_skl
| nil = sK50_skl )
& ! [Z] :
( ! [X2] :
( ~ leq(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) )
& totalorderedP(sK49_skl)
& app(sK49_skl,sK51_skl) = sK50_skl
& ssList(sK51_skl)
& neq(sK48_skl,nil)
& 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)],[f416]) ).
fof(f420,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f421,plain,
ssList(sK50_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f422,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f423,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f424,plain,
neq(sK48_skl,nil),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f425,plain,
ssList(sK51_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f426,plain,
app(sK49_skl,sK51_skl) = sK50_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f429,plain,
( nil != sK49_skl
| nil = sK50_skl ),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f430,plain,
( ~ frontsegP(sK48_skl,sK47_skl)
| ~ neq(sK47_skl,nil) ),
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(f434,definition,
( sQ1_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f437,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f429,f431,f434]) ).
fof(f438,definition,
( sQ2_spl
<=> neq(sK47_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f440,plain,
( sQ2_spl
| ~ neq(sK47_skl,nil) ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f441,definition,
( sQ3_spl
<=> frontsegP(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( sQ3_spl
| ~ frontsegP(sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f430,f438,f441]) ).
fof(f449,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f124]) ).
fof(f460,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f461,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f460]) ).
fof(f479,plain,
neq(sK50_skl,nil),
inference(forward_demodulation,[status(thm)],[f422,f424]) ).
fof(f480,plain,
( ~ sQ0_spl
| neq(sK50_skl,sK50_skl) ),
inference(forward_demodulation,[status(thm)],[f432,f479]) ).
fof(f481,plain,
( sQ2_spl
| ~ neq(sK49_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f423,f440]) ).
fof(f496,plain,
( sQ3_spl
| ~ frontsegP(sK50_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f422,f443]) ).
fof(f497,plain,
( sQ3_spl
| ~ frontsegP(sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f496]) ).
fof(f508,definition,
( sQ8_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f510,plain,
( sQ8_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f508]) ).
fof(f514,definition,
( sQ10_spl
<=> ssList(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f516,plain,
( sQ10_spl
| ~ ssList(sK51_skl) ),
inference(component_clause,[status(thm)],[f514]) ).
fof(f518,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f516,f425]) ).
fof(f519,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f518]) ).
fof(f520,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f510,f421]) ).
fof(f521,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f520]) ).
fof(f525,plain,
( ~ ssList(sK51_skl)
| frontsegP(sK50_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(app(sK49_skl,sK51_skl)) ),
inference(paramodulation,[status(thm)],[f426,f449]) ).
fof(f526,definition,
( sQ11_spl
<=> ssList(app(sK49_skl,sK51_skl)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f528,plain,
( sQ11_spl
| ~ ssList(app(sK49_skl,sK51_skl)) ),
inference(component_clause,[status(thm)],[f526]) ).
fof(f529,definition,
( sQ12_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f531,plain,
( sQ12_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f529]) ).
fof(f532,definition,
( sQ13_spl
<=> frontsegP(sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f533,plain,
( ~ sQ13_spl
| frontsegP(sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f532]) ).
fof(f535,plain,
( ~ sQ10_spl
| sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f525,f526,f529,f532,f514]) ).
fof(f536,plain,
( ~ sQ13_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f533,f497]) ).
fof(f537,plain,
( ~ sQ13_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f536]) ).
fof(f538,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f531,f420]) ).
fof(f539,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f538]) ).
fof(f540,plain,
( sQ11_spl
| ~ ssList(sK50_skl) ),
inference(forward_demodulation,[status(thm)],[f426,f528]) ).
fof(f541,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f540,f421]) ).
fof(f542,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f541]) ).
fof(f546,plain,
( sQ2_spl
| sK49_skl = nil
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f481,f220]) ).
fof(f548,definition,
( sQ14_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f550,plain,
( sQ14_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f548]) ).
fof(f551,plain,
( sQ2_spl
| sQ1_spl
| ~ sQ14_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f546,f529,f548,f434,f438]) ).
fof(f556,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f550,f223]) ).
fof(f557,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f556]) ).
fof(f586,plain,
( ~ sQ0_spl
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f480,f461]) ).
fof(f588,plain,
( ~ sQ0_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f586,f508,f431]) ).
fof(f589,plain,
$false,
inference(sat_refutation,[status(thm)],[f437,f444,f519,f521,f535,f537,f539,f542,f551,f557,f588]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC104+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.47 % Computer : n012.cluster.edu
% 0.04/0.47 % Model : x86_64 x86_64
% 0.04/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.47 % Memory : 8046.5625MB
% 0.04/0.47 % OS : Linux 6.8.0-71-generic
% 0.04/0.47 % CPULimit : 300
% 0.04/0.47 % WCLimit : 300
% 0.04/0.47 % DateTime : Mon Sep 21 07:55:52 UTC 2026
% 0.04/0.47 % CPUTime :
% 0.04/0.48 % Drodi V4.1.1
% 0.04/0.50 % Refutation found
% 0.04/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.04/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.54 % Elapsed time: 0.048974 seconds
% 0.21/0.54 % CPU time: 0.111168 seconds
% 0.21/0.54 % Total memory used: 110.889 MB
% 0.21/0.54 % Net memory used: 110.738 MB
%------------------------------------------------------------------------------