%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC018+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 02:39:36 PM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 7
% Syntax : Number of formulae : 72 ( 16 unt; 1 def)
% Number of atoms : 337 ( 104 equ)
% Maximal formula atoms : 23 ( 4 avg)
% Number of connectives : 428 ( 163 ~; 162 |; 80 &)
% ( 7 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 106 ( 80 !; 26 ?)
% 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(f42,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [U] :
( ssList(U)
=> ( frontsegP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( ? [X3] :
( frontsegP(U,X3)
& frontsegP(V,X3)
& neq(X3,nil)
& ssList(X3) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( app(X2,cons(Z,nil)) = W
& ssList(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ equalelemsP(W)
| app(W,Y) != X ) )
| 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)
=> ( ( ( ? [X3] :
( frontsegP(U,X3)
& frontsegP(V,X3)
& neq(X3,nil)
& ssList(X3) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( nil = W
& nil != X )
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( app(X2,cons(Z,nil)) = W
& ssList(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ equalelemsP(W)
| app(W,Y) != X ) )
| 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(f285,plain,
! [U] :
( frontsegP(U,U)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f286,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f285]) ).
fof(f296,plain,
! [U] :
( ( frontsegP(nil,U)
<=> nil = U )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f297,plain,
! [U] :
( ( ( nil != U
| frontsegP(nil,U) )
& ( nil = U
| ~ frontsegP(nil,U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f296]) ).
fof(f298,plain,
! [X0] :
( nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f297]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ! [X3] :
( ~ frontsegP(U,X3)
| ~ frontsegP(V,X3)
| ~ neq(X3,nil)
| ~ ssList(X3) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& ( nil != W
| nil = X )
& ? [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( app(X2,cons(Z,nil)) != W
| ~ ssList(X2) )
| app(cons(Z,nil),X1) != Y
| ~ ssList(X1) )
| ~ ssItem(Z) )
& equalelemsP(W)
& app(W,Y) = X
& ssList(Y) )
& 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] :
( ( ( ! [X3] :
( ~ frontsegP(U,X3)
| ~ frontsegP(V,X3)
| ~ neq(X3,nil)
| ~ ssList(X3) )
& neq(V,nil) )
| sP0_prd(V,U) )
& ( nil != W
| nil = X )
& ? [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( app(X2,cons(Z,nil)) != W
| ~ ssList(X2) )
| app(cons(Z,nil),X1) != Y
| ~ ssList(X1) )
| ~ ssItem(Z) )
& equalelemsP(W)
& app(W,Y) = X
& ssList(Y) )
& 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] :
( ? [X] :
( ( ( ! [X3] :
( ~ frontsegP(U,X3)
| ~ frontsegP(V,X3)
| ~ neq(X3,nil)
| ~ ssList(X3) )
& neq(V,nil) )
| sP0_prd(V,U) )
& ( nil != W
| nil = X )
& ? [Y] :
( ! [Z] :
( ! [X2] :
( app(X2,cons(Z,nil)) != W
| ~ ssList(X2) )
| ! [X1] :
( app(cons(Z,nil),X1) != Y
| ~ ssList(X1) )
| ~ ssItem(Z) )
& equalelemsP(W)
& app(W,Y) = X
& ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(miniscoping,[status(thm)],[f417]) ).
fof(f419,plain,
( ( ( ! [X3] :
( ~ frontsegP(sK47_skl,X3)
| ~ frontsegP(sK48_skl,X3)
| ~ neq(X3,nil)
| ~ ssList(X3) )
& neq(sK48_skl,nil) )
| sP0_prd(sK48_skl,sK47_skl) )
& ( nil != sK49_skl
| nil = sK50_skl )
& ! [Z] :
( ! [X2] :
( app(X2,cons(Z,nil)) != sK49_skl
| ~ ssList(X2) )
| ! [X1] :
( app(cons(Z,nil),X1) != sK51_skl
| ~ ssList(X1) )
| ~ ssItem(Z) )
& equalelemsP(sK49_skl)
& app(sK49_skl,sK51_skl) = sK50_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]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl)],[f418]) ).
fof(f421,plain,
ssList(sK48_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f422,plain,
ssList(sK49_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,
ssList(sK51_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f427,plain,
app(sK49_skl,sK51_skl) = sK50_skl,
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f430,plain,
( nil != sK49_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] :
( ~ frontsegP(sK47_skl,X0)
| ~ frontsegP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(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(f442,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f124]) ).
fof(f453,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f454,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f453]) ).
fof(f468,plain,
! [X0] : ~ sP0_prd(X0,nil),
inference(destructive_equality_resolution,[status(thm)],[f436]) ).
fof(f473,plain,
app(sK49_skl,sK51_skl) = sK48_skl,
inference(forward_demodulation,[status(thm)],[f424,f427]) ).
fof(f475,plain,
( nil != sK49_skl
| nil = sK48_skl ),
inference(forward_demodulation,[status(thm)],[f424,f430]) ).
fof(f478,plain,
( ~ ssList(sK51_skl)
| frontsegP(sK48_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(app(sK49_skl,sK51_skl)) ),
inference(paramodulation,[status(thm)],[f473,f442]) ).
fof(f479,plain,
( ~ ssList(sK51_skl)
| frontsegP(sK48_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK48_skl) ),
inference(forward_demodulation,[status(thm)],[f473,f478]) ).
fof(f480,plain,
( ~ ssList(sK51_skl)
| frontsegP(sK48_skl,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f479,f421]) ).
fof(f481,plain,
( neq(sK48_skl,nil)
| sP0_prd(sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f425,f431]) ).
fof(f483,plain,
( ~ ssList(sK51_skl)
| frontsegP(sK48_skl,sK49_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f480,f422]) ).
fof(f484,plain,
! [X0] :
( ~ frontsegP(sK47_skl,X0)
| ~ frontsegP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0)
| sP0_prd(sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f425,f432]) ).
fof(f485,plain,
! [X0] :
( ~ frontsegP(sK49_skl,X0)
| ~ frontsegP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0)
| sP0_prd(sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f425,f484]) ).
fof(f486,plain,
! [X0] :
( nil = sK48_skl
| ~ frontsegP(sK49_skl,X0)
| ~ frontsegP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f485,f435]) ).
fof(f501,plain,
! [X0] :
( X0 = nil
| ~ ssList(nil)
| ~ ssList(X0)
| nil = sK48_skl
| ~ frontsegP(sK49_skl,X0)
| ~ frontsegP(sK48_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f486,f220]) ).
fof(f505,plain,
! [X0] :
( X0 = nil
| ~ ssList(nil)
| nil = sK48_skl
| ~ frontsegP(sK49_skl,X0)
| ~ frontsegP(sK48_skl,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f501]) ).
fof(f506,plain,
! [X0] :
( X0 = nil
| nil = sK48_skl
| ~ frontsegP(sK49_skl,X0)
| ~ frontsegP(sK48_skl,X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f505,f223]) ).
fof(f508,plain,
( ~ ssList(sK49_skl)
| sK49_skl = nil
| nil = sK48_skl
| ~ frontsegP(sK48_skl,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f506,f286]) ).
fof(f509,plain,
( sK49_skl = nil
| nil = sK48_skl
| ~ frontsegP(sK48_skl,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f508]) ).
fof(f510,plain,
( sK49_skl = nil
| nil = sK48_skl
| ~ frontsegP(sK48_skl,sK49_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f509,f422]) ).
fof(f519,plain,
( nil = sK48_skl
| ~ frontsegP(sK48_skl,sK49_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f510,f475]) ).
fof(f520,plain,
( ~ ssList(sK51_skl)
| nil = sK48_skl ),
inference(resolution,[status(thm)],[f519,f483]) ).
fof(f521,plain,
nil = sK48_skl,
inference(forward_subsumption_resolution,[status(thm)],[f520,f426]) ).
fof(f527,plain,
( ~ ssList(sK51_skl)
| frontsegP(nil,sK49_skl) ),
inference(backward_demodulation,[status(thm)],[f521,f483]) ).
fof(f529,plain,
( neq(nil,nil)
| sP0_prd(sK48_skl,sK49_skl) ),
inference(backward_demodulation,[status(thm)],[f521,f481]) ).
fof(f535,plain,
frontsegP(nil,sK49_skl),
inference(forward_subsumption_resolution,[status(thm)],[f527,f426]) ).
fof(f536,plain,
( neq(nil,nil)
| sP0_prd(nil,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f521,f529]) ).
fof(f542,plain,
( nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f535,f298]) ).
fof(f543,plain,
nil = sK49_skl,
inference(forward_subsumption_resolution,[status(thm)],[f542,f422]) ).
fof(f566,plain,
( neq(nil,nil)
| sP0_prd(nil,nil) ),
inference(forward_demodulation,[status(thm)],[f543,f536]) ).
fof(f567,plain,
neq(nil,nil),
inference(forward_subsumption_resolution,[status(thm)],[f566,f468]) ).
fof(f568,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[f567,f454]) ).
fof(f570,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f568,f223]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC018+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.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 07:49:27 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.058330 seconds
% 0.12/0.42 % CPU time: 0.168488 seconds
% 0.12/0.42 % Total memory used: 69.763 MB
% 0.12/0.42 % Net memory used: 69.627 MB
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