%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC387+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 : n004.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 02:41:02 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 17
% Syntax : Number of formulae : 76 ( 11 unt; 13 def)
% Number of atoms : 247 ( 72 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 283 ( 112 ~; 104 |; 35 &)
% ( 15 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 14 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 48 ( 41 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssItem(X)
=> ( cons(W,U) = cons(X,V)
=> ( V = U
& W = X ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( neq(X,nil)
& ! [Z] :
( ssItem(Z)
=> ( ~ memberP(X,Z)
| cons(Z,nil) != W ) ) )
| ( nil = U
& nil = V )
| ( nil = X
& nil != W )
| ? [Y] :
( memberP(V,Y)
& cons(Y,nil) = U
& ssItem(Y) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( neq(X,nil)
& ! [Z] :
( ssItem(Z)
=> ( ~ memberP(X,Z)
| cons(Z,nil) != W ) ) )
| ( nil = U
& nil = V )
| ( nil = X
& nil != W )
| ? [Y] :
( memberP(V,Y)
& cons(Y,nil) = U
& ssItem(Y) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
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(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(f226,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( ( V = U
& W = X )
| cons(W,U) != cons(X,V)
| ~ ssItem(X) )
| ~ ssItem(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f227,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ neq(X,nil)
| ? [Z] :
( memberP(X,Z)
& cons(Z,nil) = W
& ssItem(Z) ) )
& ( nil != U
| nil != V )
& ( nil != X
| nil = W )
& ! [Y] :
( ~ memberP(V,Y)
| cons(Y,nil) != U
| ~ ssItem(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( ( ~ neq(sK50_skl,nil)
| ( memberP(sK50_skl,sK51_skl)
& cons(sK51_skl,nil) = sK49_skl
& ssItem(sK51_skl) ) )
& ( nil != sK47_skl
| nil != sK48_skl )
& ( nil != sK50_skl
| nil = sK49_skl )
& ! [Y] :
( ~ memberP(sK48_skl,Y)
| cons(Y,nil) != sK47_skl
| ~ ssItem(Y) )
& 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(Z,sK51_skl)],[f415]) ).
fof(f419,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f420,plain,
ssList(sK50_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f421,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f422,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f423,plain,
! [X0] :
( ~ memberP(sK48_skl,X0)
| cons(X0,nil) != sK47_skl
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
( nil != sK50_skl
| nil = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f425,plain,
( nil != sK47_skl
| nil != sK48_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f426,plain,
( ~ neq(sK50_skl,nil)
| ssItem(sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f427,plain,
( ~ neq(sK50_skl,nil)
| cons(sK51_skl,nil) = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f428,plain,
( ~ neq(sK50_skl,nil)
| memberP(sK50_skl,sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f429,definition,
( sQ0_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f430,plain,
( ~ sQ0_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f429]) ).
fof(f432,definition,
( sQ1_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f433,plain,
( ~ sQ1_spl
| nil = sK50_skl ),
inference(component_clause,[status(thm)],[f432]) ).
fof(f435,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f424,f429,f432]) ).
fof(f436,definition,
( sQ2_spl
<=> nil = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f438,plain,
( sQ2_spl
| nil != sK48_skl ),
inference(component_clause,[status(thm)],[f436]) ).
fof(f439,definition,
( sQ3_spl
<=> nil = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f441,plain,
( sQ3_spl
| nil != sK47_skl ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f442,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f425,f436,f439]) ).
fof(f443,definition,
( sQ4_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f446,definition,
( sQ5_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f448,plain,
( sQ5_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f449,plain,
( ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f426,f443,f446]) ).
fof(f450,definition,
( sQ6_spl
<=> cons(sK51_skl,nil) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f451,plain,
( ~ sQ6_spl
| cons(sK51_skl,nil) = sK49_skl ),
inference(component_clause,[status(thm)],[f450]) ).
fof(f453,plain,
( ~ sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f427,f450,f446]) ).
fof(f454,definition,
( sQ7_spl
<=> memberP(sK50_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( ~ sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f428,f454,f446]) ).
fof(f490,plain,
( sQ2_spl
| nil != sK50_skl ),
inference(forward_demodulation,[status(thm)],[f421,f438]) ).
fof(f512,plain,
( sQ5_spl
| sK50_skl = nil
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f448,f220]) ).
fof(f514,definition,
( sQ11_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f516,plain,
( sQ11_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f514]) ).
fof(f517,definition,
( sQ12_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f519,plain,
( sQ12_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f517]) ).
fof(f520,plain,
( sQ5_spl
| sQ1_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f512,f514,f517,f432,f446]) ).
fof(f525,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f519,f223]) ).
fof(f526,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f525]) ).
fof(f527,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f516,f420]) ).
fof(f528,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f527]) ).
fof(f529,plain,
( sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f490,f432,f436]) ).
fof(f531,plain,
! [X0] :
( ~ memberP(sK48_skl,X0)
| cons(X0,nil) != sK49_skl
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f422,f423]) ).
fof(f532,plain,
! [X0] :
( ~ memberP(sK50_skl,X0)
| cons(X0,nil) != sK49_skl
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f421,f531]) ).
fof(f544,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| sK47_skl = sK50_skl ),
inference(backward_demodulation,[status(thm)],[f545,f422]) ).
fof(f545,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| sK50_skl = sK49_skl ),
inference(forward_demodulation,[status(thm)],[f433,f430]) ).
fof(f546,plain,
( sQ3_spl
| ~ sQ1_spl
| sK50_skl != sK47_skl ),
inference(forward_demodulation,[status(thm)],[f433,f441]) ).
fof(f547,plain,
! [X0,X1] :
( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[f227]) ).
fof(f548,definition,
! [X0] :
( sQ14_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f549,plain,
! [X0] :
( ~ sQ14_spl
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f548]) ).
fof(f551,definition,
! [X1] :
( sQ15_spl
<=> ( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f554,plain,
( sQ15_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f547,f548,f551]) ).
fof(f555,plain,
! [X0] :
( ~ sQ14_spl
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f549]) ).
fof(f556,plain,
( ~ sQ14_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f420,f555]) ).
fof(f557,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f556]) ).
fof(f558,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f544,f546]) ).
fof(f559,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f558]) ).
fof(f561,definition,
( sQ16_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f563,plain,
( sQ16_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f561]) ).
fof(f568,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f563,f419]) ).
fof(f569,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f568]) ).
fof(f571,plain,
( ~ sQ6_spl
| ~ memberP(sK50_skl,sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f532,f451]) ).
fof(f574,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f571,f443,f454,f450]) ).
fof(f589,plain,
$false,
inference(sat_refutation,[status(thm)],[f435,f442,f449,f453,f457,f520,f526,f528,f529,f554,f557,f559,f569,f574]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC387+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n004.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 08:20:36 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.055961 seconds
% 0.13/0.41 % CPU time: 0.153822 seconds
% 0.13/0.41 % Total memory used: 89.767 MB
% 0.13/0.41 % Net memory used: 89.654 MB
%------------------------------------------------------------------------------