%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC378+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 : n016.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 02:41:00 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 2
% Syntax : Number of formulae : 53 ( 13 unt; 0 def)
% Number of atoms : 238 ( 26 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 307 ( 122 ~; 130 |; 42 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 70 ( 56 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f36,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,U) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ! [X1] :
( ( memberP(U,X1)
& memberP(V,X1) )
| ( ~ memberP(U,X1)
& ~ memberP(V,X1) )
| ~ ssItem(X1) )
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( app(Z,Y) != W
| app(Y,Z) != X
| ~ ssList(Z) ) )
| 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] :
( ( memberP(U,X1)
& memberP(V,X1) )
| ( ~ memberP(U,X1)
& ~ memberP(V,X1) )
| ~ ssItem(X1) )
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( app(Z,Y) != W
| app(Y,Z) != X
| ~ ssList(Z) ) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f268,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,U) ) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f269,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( ( ( ~ memberP(W,U)
& ~ memberP(V,U) )
| memberP(app(V,W),U) )
& ( memberP(W,U)
| memberP(V,U)
| ~ memberP(app(V,W),U) ) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f268]) ).
fof(f270,plain,
! [X0,X1,X2] :
( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f271,plain,
! [X0,X1,X2] :
( ~ memberP(X1,X0)
| memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f272,plain,
! [X0,X1,X2] :
( ~ memberP(X2,X0)
| memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ? [X1] :
( ( ~ memberP(U,X1)
| ~ memberP(V,X1) )
& ( memberP(U,X1)
| memberP(V,X1) )
& ssItem(X1) )
& ? [Y] :
( ? [Z] :
( app(Z,Y) = W
& app(Y,Z) = X
& ssList(Z) )
& ssList(Y) )
& 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] :
( ? [X1] :
( ( ~ memberP(U,X1)
| ~ memberP(V,X1) )
& ( memberP(U,X1)
| memberP(V,X1) )
& ssItem(X1) )
& ? [X] :
( ? [Y] :
( ? [Z] :
( app(Z,Y) = W
& app(Y,Z) = X
& ssList(Z) )
& ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(miniscoping,[status(thm)],[f415]) ).
fof(f417,plain,
( ( ~ memberP(sK47_skl,sK53_skl)
| ~ memberP(sK48_skl,sK53_skl) )
& ( memberP(sK47_skl,sK53_skl)
| memberP(sK48_skl,sK53_skl) )
& ssItem(sK53_skl)
& app(sK52_skl,sK51_skl) = sK49_skl
& app(sK51_skl,sK52_skl) = sK50_skl
& ssList(sK52_skl)
& ssList(sK51_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,sK53_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),skolemize(X1,sK53_skl)],[f416]) ).
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,
ssList(sK51_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f425,plain,
ssList(sK52_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f426,plain,
app(sK51_skl,sK52_skl) = sK50_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f427,plain,
app(sK52_skl,sK51_skl) = sK49_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f428,plain,
ssItem(sK53_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f429,plain,
( memberP(sK47_skl,sK53_skl)
| memberP(sK48_skl,sK53_skl) ),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f430,plain,
( ~ memberP(sK47_skl,sK53_skl)
| ~ memberP(sK48_skl,sK53_skl) ),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f464,plain,
app(sK51_skl,sK52_skl) = sK48_skl,
inference(forward_demodulation,[status(thm)],[f422,f426]) ).
fof(f466,plain,
app(sK52_skl,sK51_skl) = sK47_skl,
inference(forward_demodulation,[status(thm)],[f423,f427]) ).
fof(f477,plain,
! [X0] :
( memberP(sK51_skl,X0)
| memberP(sK52_skl,X0)
| ~ memberP(sK47_skl,X0)
| ~ ssList(sK51_skl)
| ~ ssList(sK52_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f466,f270]) ).
fof(f478,plain,
! [X0] :
( memberP(sK52_skl,X0)
| memberP(sK51_skl,X0)
| ~ memberP(sK48_skl,X0)
| ~ ssList(sK52_skl)
| ~ ssList(sK51_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f464,f270]) ).
fof(f480,plain,
! [X0] :
( memberP(sK51_skl,X0)
| memberP(sK52_skl,X0)
| ~ memberP(sK47_skl,X0)
| ~ ssList(sK51_skl)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f477,f425]) ).
fof(f481,plain,
! [X0] :
( memberP(sK52_skl,X0)
| memberP(sK51_skl,X0)
| ~ memberP(sK48_skl,X0)
| ~ ssList(sK52_skl)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f478,f424]) ).
fof(f485,plain,
! [X0] :
( memberP(sK51_skl,X0)
| memberP(sK52_skl,X0)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f480,f424]) ).
fof(f486,plain,
! [X0] :
( memberP(sK52_skl,X0)
| memberP(sK51_skl,X0)
| ~ memberP(sK48_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f481,f425]) ).
fof(f488,plain,
! [X0] :
( ~ memberP(sK52_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssList(sK51_skl)
| ~ ssList(sK52_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f466,f271]) ).
fof(f489,plain,
! [X0] :
( ~ memberP(sK51_skl,X0)
| memberP(sK48_skl,X0)
| ~ ssList(sK52_skl)
| ~ ssList(sK51_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f464,f271]) ).
fof(f490,plain,
! [X0] :
( ~ memberP(sK52_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssList(sK51_skl)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f488,f425]) ).
fof(f491,plain,
! [X0] :
( ~ memberP(sK51_skl,X0)
| memberP(sK48_skl,X0)
| ~ ssList(sK52_skl)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f489,f424]) ).
fof(f501,plain,
! [X0] :
( ~ memberP(sK52_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f490,f424]) ).
fof(f505,plain,
! [X0] :
( ~ memberP(sK51_skl,X0)
| memberP(sK48_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f491,f425]) ).
fof(f510,plain,
! [X0] :
( ~ memberP(sK51_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssList(sK51_skl)
| ~ ssList(sK52_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f466,f272]) ).
fof(f511,plain,
! [X0] :
( ~ memberP(sK52_skl,X0)
| memberP(sK48_skl,X0)
| ~ ssList(sK52_skl)
| ~ ssList(sK51_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f464,f272]) ).
fof(f512,plain,
! [X0] :
( ~ memberP(sK51_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssList(sK51_skl)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f510,f425]) ).
fof(f513,plain,
! [X0] :
( ~ memberP(sK52_skl,X0)
| memberP(sK48_skl,X0)
| ~ ssList(sK52_skl)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f511,f424]) ).
fof(f515,plain,
! [X0] :
( ~ memberP(sK51_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f512,f424]) ).
fof(f516,plain,
! [X0] :
( memberP(sK52_skl,X0)
| ~ memberP(sK48_skl,X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f515,f486]) ).
fof(f518,plain,
! [X0] :
( memberP(sK52_skl,X0)
| ~ memberP(sK48_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f516]) ).
fof(f519,plain,
! [X0] :
( ~ memberP(sK48_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f518,f501]) ).
fof(f520,plain,
( memberP(sK47_skl,sK53_skl)
| memberP(sK47_skl,sK53_skl)
| ~ ssItem(sK53_skl) ),
inference(resolution,[status(thm)],[f519,f429]) ).
fof(f521,plain,
( memberP(sK47_skl,sK53_skl)
| ~ ssItem(sK53_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f520]) ).
fof(f522,plain,
memberP(sK47_skl,sK53_skl),
inference(forward_subsumption_resolution,[status(thm)],[f521,f428]) ).
fof(f523,plain,
~ memberP(sK48_skl,sK53_skl),
inference(backward_subsumption_resolution,[status(thm)],[f430,f522]) ).
fof(f524,plain,
! [X0] :
( ~ memberP(sK52_skl,X0)
| memberP(sK48_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f513,f425]) ).
fof(f526,plain,
! [X0] :
( memberP(sK51_skl,X0)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0)
| memberP(sK48_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f524,f485]) ).
fof(f527,plain,
! [X0] :
( memberP(sK51_skl,X0)
| ~ memberP(sK47_skl,X0)
| memberP(sK48_skl,X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f526]) ).
fof(f528,plain,
! [X0] :
( ~ memberP(sK47_skl,X0)
| memberP(sK48_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f527,f505]) ).
fof(f529,plain,
( ~ memberP(sK47_skl,sK53_skl)
| ~ ssItem(sK53_skl) ),
inference(resolution,[status(thm)],[f528,f523]) ).
fof(f531,plain,
~ memberP(sK47_skl,sK53_skl),
inference(forward_subsumption_resolution,[status(thm)],[f529,f428]) ).
fof(f532,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f531,f522]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC378+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 08:24:22 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.063144 seconds
% 0.13/0.43 % CPU time: 0.179652 seconds
% 0.13/0.43 % Total memory used: 110.970 MB
% 0.13/0.43 % Net memory used: 110.769 MB
%------------------------------------------------------------------------------