%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC182+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 : n018.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 02:40:17 PM UTC 2026
% Result : Theorem 0.19s 0.49s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 101 ( 14 unt; 13 def)
% Number of atoms : 295 ( 62 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 327 ( 133 ~; 129 |; 28 &)
% ( 15 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 14 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 61 ( 54 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f83,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil = app(U,V)
<=> ( nil = U
& nil = V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(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)
=> ( ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( ( ~ memberP(X1,Y)
& ~ memberP(Z,Y) )
| app(app(Z,cons(Y,nil)),X1) != U ) ) ) )
| U != W
| V != X
| nil != W ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( ( ~ memberP(X1,Y)
& ~ memberP(Z,Y) )
| app(app(Z,cons(Y,nil)),X1) != U ) ) ) )
| U != W
| V != X
| nil != W ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f221,plain,
! [U] :
( ! [V] :
( ssList(cons(V,U))
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f222,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f244,plain,
! [U] :
( ! [V] :
( ssList(app(U,V))
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f245,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f244]) ).
fof(f278,plain,
! [U] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f279,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f278]) ).
fof(f383,plain,
! [U] :
( ! [V] :
( ( nil = app(U,V)
<=> ( nil = U
& nil = V ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f83]) ).
fof(f384,plain,
! [U] :
( ! [V] :
( ( ( nil != U
| nil != V
| nil = app(U,V) )
& ( ( nil = U
& nil = V )
| nil != app(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f383]) ).
fof(f385,plain,
! [X0,X1] :
( nil = X1
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f386,plain,
! [X0,X1] :
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f388,plain,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f84]) ).
fof(f389,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f388]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( ? [X1] :
( ( memberP(X1,Y)
| memberP(Z,Y) )
& app(app(Z,cons(Y,nil)),X1) = U
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
& U = W
& V = X
& nil = W
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( ( memberP(sK53_skl,sK51_skl)
| memberP(sK52_skl,sK51_skl) )
& app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl) = sK47_skl
& ssList(sK53_skl)
& ssList(sK52_skl)
& ssItem(sK51_skl)
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& nil = sK49_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)],[f415]) ).
fof(f419,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f421,plain,
nil = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f423,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
ssItem(sK51_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f425,plain,
ssList(sK52_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f426,plain,
ssList(sK53_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f427,plain,
app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl) = sK47_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f428,plain,
( memberP(sK53_skl,sK51_skl)
| memberP(sK52_skl,sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f429,definition,
( sQ0_spl
<=> memberP(sK52_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f430,plain,
( ~ sQ0_spl
| memberP(sK52_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f429]) ).
fof(f432,definition,
( sQ1_spl
<=> memberP(sK53_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f433,plain,
( ~ sQ1_spl
| memberP(sK53_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f432]) ).
fof(f435,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f428,f429,f432]) ).
fof(f469,plain,
! [X0] :
( ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f421,f279]) ).
fof(f471,plain,
! [X0] :
( app(X0,sK49_skl) = X0
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f421,f389]) ).
fof(f482,plain,
app(app(sK52_skl,cons(sK51_skl,sK49_skl)),sK53_skl) = sK47_skl,
inference(forward_demodulation,[status(thm)],[f421,f427]) ).
fof(f483,plain,
app(app(sK52_skl,cons(sK51_skl,sK49_skl)),sK53_skl) = sK49_skl,
inference(forward_demodulation,[status(thm)],[f423,f482]) ).
fof(f486,definition,
( sQ2_spl
<=> ssList(app(sK52_skl,cons(sK51_skl,sK49_skl))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f487,plain,
( ~ sQ2_spl
| ssList(app(sK52_skl,cons(sK51_skl,sK49_skl))) ),
inference(component_clause,[status(thm)],[f486]) ).
fof(f488,plain,
( sQ2_spl
| ~ ssList(app(sK52_skl,cons(sK51_skl,sK49_skl))) ),
inference(component_clause,[status(thm)],[f486]) ).
fof(f489,definition,
( sQ3_spl
<=> ssList(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f491,plain,
( sQ3_spl
| ~ ssList(sK53_skl) ),
inference(component_clause,[status(thm)],[f489]) ).
fof(f492,definition,
( sQ4_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f494,plain,
( sQ4_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f492]) ).
fof(f563,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f491,f426]) ).
fof(f564,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f563]) ).
fof(f568,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f494,f419]) ).
fof(f569,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f568]) ).
fof(f570,plain,
( sQ2_spl
| ~ ssList(cons(sK51_skl,sK49_skl))
| ~ ssList(sK52_skl) ),
inference(resolution,[status(thm)],[f488,f245]) ).
fof(f571,definition,
( sQ13_spl
<=> ssList(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f573,plain,
( sQ13_spl
| ~ ssList(sK52_skl) ),
inference(component_clause,[status(thm)],[f571]) ).
fof(f574,definition,
( sQ14_spl
<=> ssList(cons(sK51_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f575,plain,
( ~ sQ14_spl
| ssList(cons(sK51_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f574]) ).
fof(f576,plain,
( sQ14_spl
| ~ ssList(cons(sK51_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f574]) ).
fof(f577,plain,
( sQ2_spl
| ~ sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f570,f571,f574,f486]) ).
fof(f578,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f573,f425]) ).
fof(f579,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f578]) ).
fof(f581,plain,
( sQ14_spl
| ~ ssItem(sK51_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f222,f576]) ).
fof(f582,definition,
( sQ15_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f584,plain,
( sQ15_spl
| ~ ssItem(sK51_skl) ),
inference(component_clause,[status(thm)],[f582]) ).
fof(f585,plain,
( sQ14_spl
| ~ sQ15_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f581,f492,f582,f574]) ).
fof(f586,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f584,f424]) ).
fof(f587,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f586]) ).
fof(f588,plain,
! [X0,X1] :
( nil = X1
| sK49_skl != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f421,f385]) ).
fof(f589,plain,
! [X0,X1] :
( sK49_skl = X1
| sK49_skl != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f421,f588]) ).
fof(f592,plain,
( sK49_skl = sK53_skl
| ~ ssList(sK53_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,sK49_skl))) ),
inference(resolution,[status(thm)],[f589,f483]) ).
fof(f603,definition,
( sQ18_spl
<=> sK49_skl = sK53_skl ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f604,plain,
( ~ sQ18_spl
| sK49_skl = sK53_skl ),
inference(component_clause,[status(thm)],[f603]) ).
fof(f606,plain,
( sQ18_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f592,f486,f489,f603]) ).
fof(f610,plain,
( ~ sQ2_spl
| ~ sQ18_spl
| ssList(app(sK52_skl,cons(sK51_skl,sK53_skl))) ),
inference(backward_demodulation,[status(thm)],[f604,f487]) ).
fof(f611,plain,
( ~ sQ14_spl
| ~ sQ18_spl
| ssList(cons(sK51_skl,sK53_skl)) ),
inference(backward_demodulation,[status(thm)],[f604,f575]) ).
fof(f621,plain,
! [X0] :
( ~ sQ18_spl
| app(X0,sK53_skl) = X0
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f604,f471]) ).
fof(f623,plain,
( ~ sQ18_spl
| app(app(sK52_skl,cons(sK51_skl,sK49_skl)),sK53_skl) = sK53_skl ),
inference(backward_demodulation,[status(thm)],[f604,f483]) ).
fof(f632,plain,
! [X0] :
( ~ sQ18_spl
| ~ memberP(sK53_skl,X0)
| ~ ssItem(X0) ),
inference(backward_demodulation,[status(thm)],[f604,f469]) ).
fof(f634,plain,
( ~ sQ18_spl
| nil = sK53_skl ),
inference(backward_demodulation,[status(thm)],[f604,f421]) ).
fof(f636,plain,
( ~ sQ18_spl
| app(app(sK52_skl,cons(sK51_skl,sK53_skl)),sK53_skl) = sK53_skl ),
inference(forward_demodulation,[status(thm)],[f604,f623]) ).
fof(f690,plain,
! [X0,X1] :
( ~ sQ18_spl
| nil = X0
| sK53_skl != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f634,f386]) ).
fof(f691,plain,
! [X0,X1] :
( ~ sQ18_spl
| sK53_skl = X0
| sK53_skl != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f634,f690]) ).
fof(f713,plain,
( ~ sQ18_spl
| sK53_skl = app(sK52_skl,cons(sK51_skl,sK53_skl))
| ~ ssList(app(sK52_skl,cons(sK51_skl,sK53_skl))) ),
inference(paramodulation,[status(thm)],[f636,f621]) ).
fof(f720,definition,
( sQ29_spl
<=> ssList(app(sK52_skl,cons(sK51_skl,sK53_skl))) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f722,plain,
( sQ29_spl
| ~ ssList(app(sK52_skl,cons(sK51_skl,sK53_skl))) ),
inference(component_clause,[status(thm)],[f720]) ).
fof(f723,definition,
( sQ30_spl
<=> sK53_skl = app(sK52_skl,cons(sK51_skl,sK53_skl)) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f724,plain,
( ~ sQ30_spl
| sK53_skl = app(sK52_skl,cons(sK51_skl,sK53_skl)) ),
inference(component_clause,[status(thm)],[f723]) ).
fof(f728,plain,
( ~ sQ18_spl
| sQ30_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f713,f720,f723,f603]) ).
fof(f744,plain,
( sQ29_spl
| ~ sQ2_spl
| ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f722,f610]) ).
fof(f745,plain,
( sQ29_spl
| ~ sQ2_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f744]) ).
fof(f749,plain,
( ~ sQ18_spl
| ~ sQ30_spl
| sK53_skl = sK52_skl
| ~ ssList(cons(sK51_skl,sK53_skl))
| ~ ssList(sK52_skl) ),
inference(resolution,[status(thm)],[f724,f691]) ).
fof(f757,definition,
( sQ34_spl
<=> ssList(cons(sK51_skl,sK53_skl)) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f759,plain,
( sQ34_spl
| ~ ssList(cons(sK51_skl,sK53_skl)) ),
inference(component_clause,[status(thm)],[f757]) ).
fof(f760,definition,
( sQ35_spl
<=> sK53_skl = sK52_skl ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f761,plain,
( ~ sQ35_spl
| sK53_skl = sK52_skl ),
inference(component_clause,[status(thm)],[f760]) ).
fof(f763,plain,
( ~ sQ18_spl
| ~ sQ30_spl
| sQ35_spl
| ~ sQ34_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f749,f571,f757,f760,f723,f603]) ).
fof(f783,plain,
( sQ34_spl
| ~ sQ14_spl
| ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f759,f611]) ).
fof(f784,plain,
( sQ34_spl
| ~ sQ14_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f783]) ).
fof(f788,plain,
( ~ sQ0_spl
| ~ sQ35_spl
| memberP(sK53_skl,sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f761,f430]) ).
fof(f789,plain,
( ~ sQ18_spl
| ~ sQ0_spl
| ~ sQ35_spl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f788,f632]) ).
fof(f790,plain,
( ~ sQ18_spl
| ~ sQ0_spl
| ~ sQ35_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f789,f582,f760,f429,f603]) ).
fof(f792,plain,
( ~ sQ18_spl
| ~ sQ1_spl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f433,f632]) ).
fof(f793,plain,
( ~ sQ18_spl
| ~ sQ1_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f792,f582,f432,f603]) ).
fof(f794,plain,
$false,
inference(sat_refutation,[status(thm)],[f435,f564,f569,f577,f579,f585,f587,f606,f728,f745,f763,f784,f790,f793]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC182+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n018.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Mon Sep 21 08:04:28 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.47 % Drodi V4.1.1
% 0.19/0.49 % Refutation found
% 0.19/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.26/0.55 % Elapsed time: 0.095853 seconds
% 0.26/0.55 % CPU time: 0.129842 seconds
% 0.26/0.55 % Total memory used: 17.512 MB
% 0.26/0.55 % Net memory used: 17.481 MB
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