%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC050+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 : n014.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 02:39:45 PM UTC 2026
% Result : Theorem 0.11s 0.44s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 64 ( 9 unt; 7 def)
% Number of atoms : 275 ( 21 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 346 ( 135 ~; 123 |; 67 &)
% ( 9 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 110 ( 94 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
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)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [Z] :
( ssList(Z)
=> ( ~ rearsegP(W,Z)
| ~ rearsegP(X,Z)
| ~ neq(Z,nil) ) )
| ? [Y] :
( rearsegP(U,Y)
& rearsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ 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)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [Z] :
( ssList(Z)
=> ( ~ rearsegP(W,Z)
| ~ rearsegP(X,Z)
| ~ neq(Z,nil) ) )
| ? [Y] :
( rearsegP(U,Y)
& rearsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil) ) )
| 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(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] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| ( ? [Z] :
( rearsegP(W,Z)
& rearsegP(X,Z)
& neq(Z,nil)
& ssList(Z) )
& ! [Y] :
( ~ rearsegP(U,Y)
| ~ rearsegP(V,Y)
| ~ neq(Y,nil)
| ~ 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,definition,
! [U,V,W,X] :
( sP0_prd(X,W,V,U)
<=> ( ? [Z] :
( rearsegP(W,Z)
& rearsegP(X,Z)
& neq(Z,nil)
& ssList(Z) )
& ! [Y] :
( ~ rearsegP(U,Y)
| ~ rearsegP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| sP0_prd(X,W,V,U) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( ~ neq(sK50_skl,nil)
& neq(sK48_skl,nil) )
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,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]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl)],[f417]) ).
fof(f422,plain,
ssList(sK50_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f423,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f424,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f425,plain,
( neq(sK48_skl,nil)
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
( ~ neq(sK50_skl,nil)
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
! [U,V,W,X] :
( ( ! [Z] :
( ~ rearsegP(W,Z)
| ~ rearsegP(X,Z)
| ~ neq(Z,nil)
| ~ ssList(Z) )
| ? [Y] :
( rearsegP(U,Y)
& rearsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ( ( ? [Z] :
( rearsegP(W,Z)
& rearsegP(X,Z)
& neq(Z,nil)
& ssList(Z) )
& ! [Y] :
( ~ rearsegP(U,Y)
| ~ rearsegP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f428,plain,
( ! [U,V,W,X] :
( ! [Z] :
( ~ rearsegP(W,Z)
| ~ rearsegP(X,Z)
| ~ neq(Z,nil)
| ~ ssList(Z) )
| ? [Y] :
( rearsegP(U,Y)
& rearsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( ? [Z] :
( rearsegP(W,Z)
& rearsegP(X,Z)
& neq(Z,nil)
& ssList(Z) )
& ! [Y] :
( ~ rearsegP(U,Y)
| ~ rearsegP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(miniscoping,[status(thm)],[f427]) ).
fof(f429,plain,
( ! [U,V,W,X] :
( ! [Z] :
( ~ rearsegP(W,Z)
| ~ rearsegP(X,Z)
| ~ neq(Z,nil)
| ~ ssList(Z) )
| ( rearsegP(U,sK52_skl(X,W,V,U))
& rearsegP(V,sK52_skl(X,W,V,U))
& neq(sK52_skl(X,W,V,U),nil)
& ssList(sK52_skl(X,W,V,U)) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( rearsegP(W,sK51_skl(X,W,V,U))
& rearsegP(X,sK51_skl(X,W,V,U))
& neq(sK51_skl(X,W,V,U),nil)
& ssList(sK51_skl(X,W,V,U))
& ! [Y] :
( ~ rearsegP(U,Y)
| ~ rearsegP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51_skl,sK52_skl]),skolemize(Z,sK51_skl(X,W,V,U)),skolemize(Y,sK52_skl(X,W,V,U))],[f428]) ).
fof(f431,plain,
! [X0,X1,X2,X3,X4] :
( ~ rearsegP(X3,X4)
| ~ rearsegP(X2,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f432,plain,
! [X0,X1,X2,X3] :
( ssList(sK51_skl(X0,X1,X2,X3))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f433,plain,
! [X0,X1,X2,X3] :
( neq(sK51_skl(X0,X1,X2,X3),nil)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f434,plain,
! [X0,X1,X2,X3] :
( rearsegP(X0,sK51_skl(X0,X1,X2,X3))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f435,plain,
! [X0,X1,X2,X3] :
( rearsegP(X1,sK51_skl(X0,X1,X2,X3))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f440,definition,
( sQ0_spl
<=> sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f441,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f443,definition,
( sQ1_spl
<=> neq(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f444,plain,
( ~ sQ1_spl
| neq(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f443]) ).
fof(f446,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f425,f440,f443]) ).
fof(f447,definition,
( sQ2_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f449,plain,
( sQ2_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f447]) ).
fof(f450,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f440,f447]) ).
fof(f466,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f467,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f466]) ).
fof(f483,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl,sK50_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f441]) ).
fof(f484,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl,sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f483]) ).
fof(f487,definition,
( sQ3_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f489,plain,
( sQ3_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f487]) ).
fof(f495,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f489,f223]) ).
fof(f496,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f495]) ).
fof(f504,plain,
! [X0] :
( ~ sQ0_spl
| ~ rearsegP(sK49_skl,X0)
| ~ rearsegP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f431,f484]) ).
fof(f520,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| ~ sP0_prd(X0,X1,X2,X3)
| ~ rearsegP(sK49_skl,sK51_skl(X0,X1,X2,X3))
| ~ rearsegP(sK50_skl,sK51_skl(X0,X1,X2,X3))
| ~ ssList(sK51_skl(X0,X1,X2,X3)) ),
inference(resolution,[status(thm)],[f504,f433]) ).
fof(f524,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| ~ sP0_prd(X0,X1,X2,X3)
| ~ rearsegP(sK49_skl,sK51_skl(X0,X1,X2,X3))
| ~ rearsegP(sK50_skl,sK51_skl(X0,X1,X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f520,f432]) ).
fof(f525,definition,
( sQ6_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f527,plain,
( sQ6_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f525]) ).
fof(f567,plain,
( ~ sQ1_spl
| neq(sK50_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f423,f444]) ).
fof(f606,plain,
( sQ2_spl
| sK50_skl = nil
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f449,f220]) ).
fof(f608,definition,
( sQ16_spl
<=> sK50_skl = nil ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f609,plain,
( ~ sQ16_spl
| sK50_skl = nil ),
inference(component_clause,[status(thm)],[f608]) ).
fof(f611,plain,
( sQ2_spl
| sQ16_spl
| ~ sQ3_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f606,f525,f487,f608,f447]) ).
fof(f616,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f527,f422]) ).
fof(f617,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f616]) ).
fof(f642,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| neq(sK50_skl,sK50_skl) ),
inference(forward_demodulation,[status(thm)],[f609,f567]) ).
fof(f643,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f642,f467]) ).
fof(f645,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f643,f525,f608,f443]) ).
fof(f1014,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sP0_prd(X0,sK49_skl,X1,X2)
| ~ sP0_prd(X0,sK49_skl,X1,X2)
| ~ rearsegP(sK50_skl,sK51_skl(X0,sK49_skl,X1,X2)) ),
inference(resolution,[status(thm)],[f524,f435]) ).
fof(f1024,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sP0_prd(X0,sK49_skl,X1,X2)
| ~ rearsegP(sK50_skl,sK51_skl(X0,sK49_skl,X1,X2)) ),
inference(duplicate_literals_removal,[status(thm)],[f1014]) ).
fof(f1030,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sP0_prd(sK50_skl,sK49_skl,X0,X1)
| ~ sP0_prd(sK50_skl,sK49_skl,X0,X1) ),
inference(resolution,[status(thm)],[f1024,f434]) ).
fof(f1039,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sP0_prd(sK50_skl,sK49_skl,X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f1030]) ).
fof(f1041,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f484,f1039]) ).
fof(f1042,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f1041]) ).
fof(f1043,plain,
$false,
inference(sat_refutation,[status(thm)],[f446,f450,f496,f611,f617,f645,f1042]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC050+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.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 07:51:05 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.11/0.44 % Refutation found
% 0.11/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.47 % Elapsed time: 0.101345 seconds
% 0.11/0.47 % CPU time: 0.399848 seconds
% 0.11/0.47 % Total memory used: 114.976 MB
% 0.11/0.47 % Net memory used: 114.483 MB
%------------------------------------------------------------------------------