%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO531+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 12:25:10 PM UTC 2026
% Result : Theorem 40.18s 5.59s
% Output : CNFRefutation 40.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 50 ( 11 unt; 7 def)
% Number of atoms : 154 ( 19 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 198 ( 94 ~; 87 |; 10 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 8 prp; 0-6 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 100 ( 97 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [Xa,Xb] : s_e(Xa,Xb,Xa,Xb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f74,axiom,
! [Xa,Xp] :
( sameside(Xa,Xp,Xa)
| Xa = Xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f203,axiom,
! [Xa1,Xb,Xa,Xc1,Xc,Xd1,Xe,Xd,Xf1,Xf] :
( congruent(Xa,Xb,Xc,Xd,Xe,Xf)
| ~ s_e3(Xa1,Xb,Xc1,Xd1,Xe,Xf1)
| ~ sameside(Xf1,Xe,Xf)
| ~ sameside(Xd1,Xe,Xd)
| ~ sameside(Xc1,Xb,Xc)
| ~ sameside(Xa1,Xb,Xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f207,conjecture,
! [Xa,Xb,Xc] :
( congruent(Xa,Xb,Xc,Xa,Xb,Xc)
| Xc = Xb
| Xa = Xb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f208,negated_conjecture,
~ ! [Xa,Xb,Xc] :
( congruent(Xa,Xb,Xc,Xa,Xb,Xc)
| Xc = Xb
| Xa = Xb ),
inference(negated_conjecture,[status(cth)],[f207]) ).
fof(f212,axiom,
! [Xa1,Xa2,Xa3,Xb1,Xb2,Xb3] :
( ( s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3)
| ~ s_e(Xa2,Xa3,Xb2,Xb3)
| ~ s_e(Xa1,Xa3,Xb1,Xb3)
| ~ s_e(Xa1,Xa2,Xb1,Xb2) )
& ( s_e(Xa2,Xa3,Xb2,Xb3)
| ~ s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3) )
& ( s_e(Xa1,Xa3,Xb1,Xb3)
| ~ s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3) )
& ( s_e(Xa1,Xa2,Xb1,Xb2)
| ~ s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f241,plain,
! [X0,X1] : s_e(X0,X1,X0,X1),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f349,plain,
! [X0,X1] :
( sameside(X0,X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f588,plain,
! [Xb,Xa,Xc,Xe,Xd,Xf] :
( congruent(Xa,Xb,Xc,Xd,Xe,Xf)
| ! [Xa1,Xc1,Xd1,Xf1] :
( ~ s_e3(Xa1,Xb,Xc1,Xd1,Xe,Xf1)
| ~ sameside(Xf1,Xe,Xf)
| ~ sameside(Xd1,Xe,Xd)
| ~ sameside(Xc1,Xb,Xc)
| ~ sameside(Xa1,Xb,Xa) ) ),
inference(miniscoping,[status(thm)],[f203]) ).
fof(f589,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ~ sameside(X7,X1,X0)
| ~ sameside(X8,X1,X2)
| ~ sameside(X9,X4,X3)
| ~ s_e3(X7,X1,X8,X9,X4,X6)
| ~ sameside(X6,X4,X5)
| congruent(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(thm)],[f588]) ).
fof(f602,plain,
? [Xa,Xb,Xc] :
( ~ congruent(Xa,Xb,Xc,Xa,Xb,Xc)
& Xc != Xb
& Xa != Xb ),
inference(pre_NNF_transformation,[status(thm)],[f208]) ).
fof(f603,plain,
( ~ congruent(sK0_skl,sK1_skl,sK2_skl,sK0_skl,sK1_skl,sK2_skl)
& sK2_skl != sK1_skl
& sK0_skl != sK1_skl ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(Xa,sK0_skl),skolemize(Xb,sK1_skl),skolemize(Xc,sK2_skl)],[f602]) ).
fof(f604,plain,
sK0_skl != sK1_skl,
inference(cnf_transformation,[status(thm)],[f603]) ).
fof(f605,plain,
sK2_skl != sK1_skl,
inference(cnf_transformation,[status(thm)],[f603]) ).
fof(f606,plain,
~ congruent(sK0_skl,sK1_skl,sK2_skl,sK0_skl,sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f603]) ).
fof(f624,plain,
( ! [Xa1,Xa2,Xa3,Xb1,Xb2,Xb3] :
( s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3)
| ~ s_e(Xa2,Xa3,Xb2,Xb3)
| ~ s_e(Xa1,Xa3,Xb1,Xb3)
| ~ s_e(Xa1,Xa2,Xb1,Xb2) )
& ! [Xa2,Xa3,Xb2,Xb3] :
( s_e(Xa2,Xa3,Xb2,Xb3)
| ! [Xa1,Xb1] : ~ s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3) )
& ! [Xa1,Xa3,Xb1,Xb3] :
( s_e(Xa1,Xa3,Xb1,Xb3)
| ! [Xa2,Xb2] : ~ s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3) )
& ! [Xa1,Xa2,Xb1,Xb2] :
( s_e(Xa1,Xa2,Xb1,Xb2)
| ! [Xa3,Xb3] : ~ s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3) ) ),
inference(miniscoping,[status(thm)],[f212]) ).
fof(f628,plain,
! [X0,X1,X2,X3,X4,X5] :
( s_e3(X4,X0,X1,X5,X2,X3)
| ~ s_e(X4,X1,X5,X3)
| ~ s_e(X4,X0,X5,X2)
| ~ s_e(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f624]) ).
fof(f741,definition,
( sQ6_spl
<=> sK1_skl = sK2_skl ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f742,plain,
( ~ sQ6_spl
| sK1_skl = sK2_skl ),
inference(component_clause,[status(thm)],[f741]) ).
fof(f744,definition,
( sQ7_spl
<=> sK1_skl = sK0_skl ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f745,plain,
( ~ sQ7_spl
| sK1_skl = sK0_skl ),
inference(component_clause,[status(thm)],[f744]) ).
fof(f751,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f742,f605]) ).
fof(f752,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f751]) ).
fof(f753,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f745,f604]) ).
fof(f754,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f753]) ).
fof(f756,plain,
! [X0,X1,X2,X3] :
( ~ sameside(X2,sK1_skl,sK0_skl)
| ~ sameside(X3,sK1_skl,sK2_skl)
| ~ s_e3(X1,sK1_skl,X0,X2,sK1_skl,X3)
| ~ sameside(X1,sK1_skl,sK0_skl)
| ~ sameside(X0,sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f589,f606]) ).
fof(f833,plain,
! [X0,X1,X2,X3] :
( ~ sameside(X2,sK1_skl,sK2_skl)
| ~ sameside(X1,sK1_skl,sK2_skl)
| ~ s_e(X0,sK1_skl,X3,sK1_skl)
| ~ s_e(X0,X1,X3,X2)
| ~ sameside(X3,sK1_skl,sK0_skl)
| ~ s_e(sK1_skl,X1,sK1_skl,X2)
| ~ sameside(X0,sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f628,f756]) ).
fof(f1238,plain,
! [X0,X1] :
( ~ s_e(X0,sK1_skl,X1,sK1_skl)
| ~ s_e(X0,sK2_skl,X1,sK2_skl)
| ~ sameside(X1,sK1_skl,sK0_skl)
| ~ s_e(sK1_skl,sK2_skl,sK1_skl,sK2_skl)
| ~ sameside(X0,sK1_skl,sK0_skl)
| sK2_skl = sK1_skl ),
inference(resolution,[status(thm)],[f349,f833]) ).
fof(f1278,definition,
! [X0,X1] :
( sQ39_spl
<=> ( ~ s_e(X0,sK1_skl,X1,sK1_skl)
| ~ s_e(X0,sK2_skl,X1,sK2_skl)
| ~ sameside(X1,sK1_skl,sK0_skl)
| ~ sameside(X0,sK1_skl,sK0_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f1279,plain,
! [X0,X1] :
( ~ sQ39_spl
| ~ sameside(X0,sK1_skl,sK0_skl)
| ~ sameside(X1,sK1_skl,sK0_skl)
| ~ s_e(X0,sK2_skl,X1,sK2_skl)
| ~ s_e(X0,sK1_skl,X1,sK1_skl) ),
inference(component_clause,[status(thm)],[f1278]) ).
fof(f1281,definition,
( sQ40_spl
<=> s_e(sK1_skl,sK2_skl,sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f1283,plain,
( sQ40_spl
| ~ s_e(sK1_skl,sK2_skl,sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f1281]) ).
fof(f1284,plain,
( ~ sQ40_spl
| sQ39_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f1238,f741,f1278,f1281]) ).
fof(f1312,plain,
( sQ40_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1283,f241]) ).
fof(f1313,plain,
sQ40_spl,
inference(contradiction_clause,[status(thm)],[f1312]) ).
fof(f1559,plain,
! [X0] :
( ~ sQ39_spl
| sK0_skl = sK1_skl
| ~ sameside(X0,sK1_skl,sK0_skl)
| ~ s_e(X0,sK2_skl,sK0_skl,sK2_skl)
| ~ s_e(X0,sK1_skl,sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f1279,f349]) ).
fof(f1564,definition,
! [X0] :
( sQ71_spl
<=> ( ~ sameside(X0,sK1_skl,sK0_skl)
| ~ s_e(X0,sK2_skl,sK0_skl,sK2_skl)
| ~ s_e(X0,sK1_skl,sK0_skl,sK1_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1565,plain,
! [X0] :
( ~ sQ71_spl
| ~ s_e(X0,sK2_skl,sK0_skl,sK2_skl)
| ~ s_e(X0,sK1_skl,sK0_skl,sK1_skl)
| ~ sameside(X0,sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f1564]) ).
fof(f1567,plain,
( ~ sQ39_spl
| sQ7_spl
| sQ71_spl ),
inference(split_clause,[status(thm)],[f1559,f1564,f744,f1278]) ).
fof(f1581,plain,
( ~ sQ71_spl
| sK0_skl = sK1_skl
| ~ s_e(sK0_skl,sK2_skl,sK0_skl,sK2_skl)
| ~ s_e(sK0_skl,sK1_skl,sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f1565,f349]) ).
fof(f1582,definition,
( sQ73_spl
<=> s_e(sK0_skl,sK1_skl,sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1584,plain,
( sQ73_spl
| ~ s_e(sK0_skl,sK1_skl,sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f1582]) ).
fof(f1585,definition,
( sQ74_spl
<=> s_e(sK0_skl,sK2_skl,sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f1587,plain,
( sQ74_spl
| ~ s_e(sK0_skl,sK2_skl,sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f1585]) ).
fof(f1588,plain,
( ~ sQ71_spl
| sQ7_spl
| ~ sQ74_spl
| ~ sQ73_spl ),
inference(split_clause,[status(thm)],[f1581,f1582,f1585,f744,f1564]) ).
fof(f1597,plain,
( sQ74_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1587,f241]) ).
fof(f1598,plain,
sQ74_spl,
inference(contradiction_clause,[status(thm)],[f1597]) ).
fof(f1599,plain,
( sQ73_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1584,f241]) ).
fof(f1600,plain,
sQ73_spl,
inference(contradiction_clause,[status(thm)],[f1599]) ).
fof(f1601,plain,
$false,
inference(sat_refutation,[status(thm)],[f752,f754,f1284,f1313,f1567,f1588,f1598,f1600]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO531+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 17:14:20 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.41 % Drodi V4.1.1
% 40.18/5.59 % Refutation found
% 40.18/5.59 % SZS status Theorem for theBenchmark: Theorem is valid
% 40.18/5.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.61/5.64 % Elapsed time: 5.248040 seconds
% 3.61/5.64 % CPU time: 41.178035 seconds
% 3.61/5.64 % Total memory used: 185.244 MB
% 3.61/5.64 % Net memory used: 171.096 MB
%------------------------------------------------------------------------------