%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC320+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 : n011.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 02:40:46 PM UTC 2026
% Result : Theorem 0.14s 15.58s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 28
% Syntax : Number of formulae : 123 ( 9 unt; 22 def)
% Number of atoms : 463 ( 133 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 578 ( 238 ~; 221 |; 75 &)
% ( 26 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 22 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 132 ( 107 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
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(f18,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( ? [X1] :
( ? [X2] :
( app(X2,cons(X1,nil)) = V
& app(cons(X1,nil),X2) = U
& ssList(X2) )
& ssItem(X1) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( neq(X,nil)
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( app(Z,cons(Y,nil)) != X
| app(cons(Y,nil),Z) != W
| ~ ssList(Z) ) ) )
| ( nil = X
& nil != W )
| 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] :
( ( ( ? [X1] :
( ? [X2] :
( app(X2,cons(X1,nil)) = V
& app(cons(X1,nil),X2) = U
& ssList(X2) )
& ssItem(X1) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( neq(X,nil)
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( app(Z,cons(Y,nil)) != X
| app(cons(Y,nil),Z) != W
| ~ ssList(Z) ) ) )
| ( nil = X
& nil != W )
| 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(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(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(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(f228,plain,
! [X0,X1,X2,X3] :
( X1 = X0
| 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] :
( ( ( ! [X1] :
( ! [X2] :
( app(X2,cons(X1,nil)) != V
| app(cons(X1,nil),X2) != U
| ~ ssList(X2) )
| ~ ssItem(X1) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& ( ~ neq(X,nil)
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = X
& app(cons(Y,nil),Z) = W
& ssList(Z) )
& ssItem(Y) ) )
& ( nil != X
| nil = W )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [U,V] :
( sP0_prd(V,U)
<=> ( nil != U
& nil = V ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ! [X1] :
( ! [X2] :
( app(X2,cons(X1,nil)) != V
| app(cons(X1,nil),X2) != U
| ~ ssList(X2) )
| ~ ssItem(X1) )
& neq(V,nil) )
| sP0_prd(V,U) )
& ( ~ neq(X,nil)
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = X
& app(cons(Y,nil),Z) = W
& ssList(Z) )
& ssItem(Y) ) )
& ( nil != X
| nil = W )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
? [U] :
( ? [V] :
( ? [W] :
( ( ( ! [X1] :
( ! [X2] :
( app(X2,cons(X1,nil)) != V
| app(cons(X1,nil),X2) != U
| ~ ssList(X2) )
| ~ ssItem(X1) )
& neq(V,nil) )
| sP0_prd(V,U) )
& ? [X] :
( ( ~ neq(X,nil)
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = X
& app(cons(Y,nil),Z) = W
& ssList(Z) )
& ssItem(Y) ) )
& ( nil != X
| nil = W )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(miniscoping,[status(thm)],[f417]) ).
fof(f419,plain,
( ( ( ! [X1] :
( ! [X2] :
( app(X2,cons(X1,nil)) != sK48_skl
| app(cons(X1,nil),X2) != sK47_skl
| ~ ssList(X2) )
| ~ ssItem(X1) )
& neq(sK48_skl,nil) )
| sP0_prd(sK48_skl,sK47_skl) )
& ( ~ neq(sK50_skl,nil)
| ( app(sK52_skl,cons(sK51_skl,nil)) = sK50_skl
& app(cons(sK51_skl,nil),sK52_skl) = sK49_skl
& ssList(sK52_skl)
& ssItem(sK51_skl) ) )
& ( nil != sK50_skl
| nil = sK49_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,sK52_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl),skolemize(Z,sK52_skl)],[f418]) ).
fof(f423,plain,
ssList(sK50_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f424,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f425,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f426,plain,
( nil != sK50_skl
| nil = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f427,plain,
( ~ neq(sK50_skl,nil)
| ssItem(sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f428,plain,
( ~ neq(sK50_skl,nil)
| ssList(sK52_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f429,plain,
( ~ neq(sK50_skl,nil)
| app(cons(sK51_skl,nil),sK52_skl) = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f430,plain,
( ~ neq(sK50_skl,nil)
| app(sK52_skl,cons(sK51_skl,nil)) = sK50_skl ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f431,plain,
( neq(sK48_skl,nil)
| sP0_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f432,plain,
! [X0,X1] :
( app(X1,cons(X0,nil)) != sK48_skl
| app(cons(X0,nil),X1) != sK47_skl
| ~ ssList(X1)
| ~ ssItem(X0)
| sP0_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f433,plain,
! [U,V] :
( ( nil = U
| nil != V
| sP0_prd(V,U) )
& ( ( nil != U
& nil = V )
| ~ sP0_prd(V,U) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f434,plain,
( ! [U,V] :
( nil = U
| nil != V
| sP0_prd(V,U) )
& ! [U,V] :
( ( nil != U
& nil = V )
| ~ sP0_prd(V,U) ) ),
inference(miniscoping,[status(thm)],[f433]) ).
fof(f435,plain,
! [X0,X1] :
( nil = X0
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f436,plain,
! [X0,X1] :
( nil != X1
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f437,plain,
! [X0,X1] :
( nil = X1
| nil != X0
| sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f438,definition,
( sQ0_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f439,plain,
( ~ sQ0_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f441,definition,
( sQ1_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( ~ sQ1_spl
| nil = sK50_skl ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f443,plain,
( sQ1_spl
| nil != sK50_skl ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f438,f441]) ).
fof(f445,definition,
( sQ2_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f448,definition,
( sQ3_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f449,plain,
( ~ sQ3_spl
| neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f448]) ).
fof(f450,plain,
( sQ3_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f448]) ).
fof(f451,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f427,f445,f448]) ).
fof(f452,definition,
( sQ4_spl
<=> ssList(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f455,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f428,f452,f448]) ).
fof(f456,definition,
( sQ5_spl
<=> app(cons(sK51_skl,nil),sK52_skl) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( ~ sQ5_spl
| app(cons(sK51_skl,nil),sK52_skl) = sK49_skl ),
inference(component_clause,[status(thm)],[f456]) ).
fof(f459,plain,
( ~ sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f429,f456,f448]) ).
fof(f460,definition,
( sQ6_spl
<=> app(sK52_skl,cons(sK51_skl,nil)) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f463,plain,
( ~ sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f430,f460,f448]) ).
fof(f464,definition,
( sQ7_spl
<=> sP0_prd(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f465,plain,
( ~ sQ7_spl
| sP0_prd(sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f467,definition,
( sQ8_spl
<=> neq(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f468,plain,
( ~ sQ8_spl
| neq(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f467]) ).
fof(f470,plain,
( sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f431,f464,f467]) ).
fof(f471,definition,
! [X0,X1] :
( sQ9_spl
<=> ( app(X1,cons(X0,nil)) != sK48_skl
| app(cons(X0,nil),X1) != sK47_skl
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f472,plain,
! [X0,X1] :
( ~ sQ9_spl
| app(X1,cons(X0,nil)) != sK48_skl
| app(cons(X0,nil),X1) != sK47_skl
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f471]) ).
fof(f474,plain,
( sQ9_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f432,f464,f471]) ).
fof(f490,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f491,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f490]) ).
fof(f505,plain,
! [X0] : ~ sP0_prd(X0,nil),
inference(destructive_equality_resolution,[status(thm)],[f436]) ).
fof(f506,plain,
! [X0] :
( nil = X0
| sP0_prd(nil,X0) ),
inference(destructive_equality_resolution,[status(thm)],[f437]) ).
fof(f510,plain,
! [X0] :
( ~ sQ0_spl
| ~ sP0_prd(X0,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f439,f505]) ).
fof(f512,plain,
( ~ sQ7_spl
| sP0_prd(sK50_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f465]) ).
fof(f513,plain,
( ~ sQ7_spl
| sP0_prd(sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f425,f512]) ).
fof(f514,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f513,f510]) ).
fof(f515,plain,
( ~ sQ7_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f514]) ).
fof(f516,plain,
( ~ sQ8_spl
| neq(sK50_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f424,f468]) ).
fof(f517,plain,
! [X0,X1] :
( ~ sQ9_spl
| app(X1,cons(X0,nil)) != sK48_skl
| app(cons(X0,nil),X1) != sK49_skl
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f425,f472]) ).
fof(f518,plain,
! [X0,X1] :
( ~ sQ9_spl
| app(X1,cons(X0,nil)) != sK50_skl
| app(cons(X0,nil),X1) != sK49_skl
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f424,f517]) ).
fof(f522,plain,
( sQ3_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f450,f516]) ).
fof(f523,plain,
( sQ3_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f522]) ).
fof(f524,plain,
( ~ sQ7_spl
| nil = sK50_skl ),
inference(resolution,[status(thm)],[f435,f513]) ).
fof(f525,plain,
( ~ sQ7_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f524,f443]) ).
fof(f526,plain,
( ~ sQ7_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f525]) ).
fof(f528,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| neq(sK50_skl,sK50_skl) ),
inference(backward_demodulation,[status(thm)],[f442,f449]) ).
fof(f550,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f528,f491]) ).
fof(f552,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f550,f423]) ).
fof(f553,plain,
( ~ sQ3_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f552]) ).
fof(f555,plain,
! [X0] :
( nil = nil
| nil = X0 ),
inference(resolution,[status(thm)],[f506,f435]) ).
fof(f556,definition,
! [X0] :
( sQ10_spl
<=> nil = X0 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f557,plain,
! [X0] :
( ~ sQ10_spl
| nil = X0 ),
inference(component_clause,[status(thm)],[f556]) ).
fof(f559,definition,
( sQ11_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f562,plain,
( sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f555,f556,f559]) ).
fof(f563,plain,
( sQ1_spl
| ~ sQ10_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f443,f557]) ).
fof(f578,plain,
( sQ1_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f563]) ).
fof(f582,plain,
( ~ singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sK4_skl(nil))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f225,f117]) ).
fof(f583,definition,
( sQ12_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f585,plain,
( sQ12_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f583]) ).
fof(f586,definition,
( sQ13_spl
<=> ssItem(sK4_skl(nil)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f589,definition,
( sQ14_spl
<=> singletonP(nil) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f592,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f582,f583,f586,f589]) ).
fof(f603,plain,
! [X0,X1] :
( ~ singletonP(cons(X1,X0))
| ~ ssList(cons(X1,X0))
| sK4_skl(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssItem(sK4_skl(cons(X1,X0)))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f227,f117]) ).
fof(f605,plain,
! [X0,X1] :
( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[f227]) ).
fof(f606,definition,
! [X0,X1] :
( sQ17_spl
<=> ( ~ singletonP(cons(X1,X0))
| ~ ssList(cons(X1,X0))
| sK4_skl(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssItem(sK4_skl(cons(X1,X0)))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f609,plain,
( sQ17_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f603,f583,f606]) ).
fof(f611,definition,
! [X0] :
( sQ18_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f612,plain,
! [X0] :
( ~ sQ18_spl
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f611]) ).
fof(f614,definition,
! [X1] :
( sQ19_spl
<=> ( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f617,plain,
( sQ19_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f605,f611,f614]) ).
fof(f618,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f585,f223]) ).
fof(f619,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f618]) ).
fof(f620,plain,
! [X0] :
( ~ sQ18_spl
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f612]) ).
fof(f622,plain,
! [X0,X1] :
( ~ singletonP(cons(X1,X0))
| ~ ssList(cons(X1,X0))
| X0 = nil
| ~ ssItem(X1)
| ~ ssItem(sK4_skl(cons(X1,X0)))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f228,f117]) ).
fof(f624,plain,
! [X0,X1] :
( X0 = X0
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[f228]) ).
fof(f625,definition,
! [X0,X1] :
( sQ20_spl
<=> ( ~ singletonP(cons(X1,X0))
| ~ ssList(cons(X1,X0))
| X0 = nil
| ~ ssItem(X1)
| ~ ssItem(sK4_skl(cons(X1,X0)))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f628,plain,
( sQ20_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f622,f583,f625]) ).
fof(f630,definition,
! [X0] :
( sQ21_spl
<=> ( X0 = X0
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f633,definition,
! [X1] :
( sQ22_spl
<=> ( ~ ssItem(X1)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f636,plain,
( sQ22_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f624,f630,f633]) ).
fof(f638,plain,
( ~ sQ18_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f223,f620]) ).
fof(f642,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f638]) ).
fof(f644,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| app(sK52_skl,cons(sK51_skl,nil)) != sK50_skl
| ~ ssList(sK52_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f518,f457]) ).
fof(f647,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f644,f445,f452,f460,f471,f456]) ).
fof(f656,plain,
$false,
inference(sat_refutation,[status(thm)],[f444,f451,f455,f459,f463,f470,f474,f515,f523,f526,f553,f562,f578,f592,f609,f617,f619,f628,f636,f642,f647]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC320+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.14/15.53 % CPULimit : 300
% 0.14/15.53 % WCLimit : 300
% 0.14/15.53 % DateTime : Mon Sep 21 08:16:25 UTC 2026
% 0.14/15.53 % CPUTime :
% 0.14/15.55 % Drodi V4.1.1
% 0.14/15.58 % Refutation found
% 0.14/15.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/15.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.43/15.61 % Elapsed time: 0.078026 seconds
% 0.43/15.61 % CPU time: 0.214421 seconds
% 0.43/15.61 % Total memory used: 110.863 MB
% 0.43/15.61 % Net memory used: 110.744 MB
%------------------------------------------------------------------------------