%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO526+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 45.35s 11.28s
% Output : CNFRefutation 45.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 20 unt; 2 def)
% Number of atoms : 115 ( 17 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 120 ( 53 ~; 45 |; 20 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 85 ( 75 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y,Z,V,Z2,V2] :
( s_e(Z,V,Z2,V2)
| ~ s_e(X,Y,Z2,V2)
| ~ s_e(X,Y,Z,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f98,axiom,
! [Xp,Xa,Xq] :
( Xq = s(Xa,Xp)
| ~ s_m(Xp,Xa,Xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f99,axiom,
! [Xa,Xp] : s(Xa,s(Xa,Xp)) = Xp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f120,axiom,
! [Xa,Xb,Xc] :
( s_r(Xa,Xb,s(Xb,Xc))
| ~ s_r(Xa,Xb,Xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f146,axiom,
! [Xa,Xb] : s_m(Xa,midpoint(Xa,Xb),Xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f194,axiom,
! [Xa,Xb,Xc,Xa1] :
( s_e(Xa,Xc,Xa1,Xc)
| ~ s_e(Xa,Xb,Xa1,Xb)
| ~ s_r(Xa1,Xb,Xc)
| ~ s_r(Xa,Xb,Xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f195,conjecture,
! [Xa,Xb,Xc,Xa1,Xc1] :
( Xc = Xc1
| Xb != midpoint(Xc,Xc1)
| s_e(Xa,Xc,Xa1,Xc1)
| ~ s_e(Xb,Xc,Xb,Xc1)
| ~ s_e(Xa,Xb,Xa1,Xb)
| ~ s_r(Xa1,Xb,Xc1)
| ~ s_r(Xa,Xb,Xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
~ ! [Xa,Xb,Xc,Xa1,Xc1] :
( Xc = Xc1
| Xb != midpoint(Xc,Xc1)
| s_e(Xa,Xc,Xa1,Xc1)
| ~ s_e(Xb,Xc,Xb,Xc1)
| ~ s_e(Xa,Xb,Xa1,Xb)
| ~ s_r(Xa1,Xb,Xc1)
| ~ s_r(Xa,Xb,Xc) ),
inference(negated_conjecture,[status(cth)],[f195]) ).
fof(f207,axiom,
! [Xa,Xb,Xc] :
( ( ~ s_e(Xa,Xc,Xa,s(Xb,Xc))
| s_r(Xa,Xb,Xc) )
& ( s_e(Xa,Xc,Xa,s(Xb,Xc))
| ~ s_r(Xa,Xb,Xc) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f213,plain,
! [Z,V,Z2,V2] :
( s_e(Z,V,Z2,V2)
| ! [X,Y] :
( ~ s_e(X,Y,Z2,V2)
| ~ s_e(X,Y,Z,V) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f214,plain,
! [X0,X1,X2,X3,X4,X5] :
( s_e(X2,X3,X4,X5)
| ~ s_e(X0,X1,X4,X5)
| ~ s_e(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f213]) ).
fof(f375,plain,
! [X0,X1,X2] :
( X2 = s(X1,X0)
| ~ s_m(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f376,plain,
! [X0,X1] : s(X0,s(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f411,plain,
! [X0,X1,X2] :
( s_r(X0,X1,s(X1,X2))
| ~ s_r(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f467,plain,
! [X0,X1] : s_m(X0,midpoint(X0,X1),X1),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f553,plain,
! [Xa,Xc,Xa1] :
( s_e(Xa,Xc,Xa1,Xc)
| ! [Xb] :
( ~ s_e(Xa,Xb,Xa1,Xb)
| ~ s_r(Xa1,Xb,Xc)
| ~ s_r(Xa,Xb,Xc) ) ),
inference(miniscoping,[status(thm)],[f194]) ).
fof(f554,plain,
! [X0,X1,X2,X3] :
( s_e(X0,X2,X3,X2)
| ~ s_e(X0,X1,X3,X1)
| ~ s_r(X3,X1,X2)
| ~ s_r(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f553]) ).
fof(f555,plain,
? [Xa,Xb,Xc,Xa1,Xc1] :
( Xc != Xc1
& Xb = midpoint(Xc,Xc1)
& ~ s_e(Xa,Xc,Xa1,Xc1)
& s_e(Xb,Xc,Xb,Xc1)
& s_e(Xa,Xb,Xa1,Xb)
& s_r(Xa1,Xb,Xc1)
& s_r(Xa,Xb,Xc) ),
inference(pre_NNF_transformation,[status(thm)],[f196]) ).
fof(f556,plain,
? [Xc,Xc1] :
( Xc != Xc1
& ? [Xb] :
( Xb = midpoint(Xc,Xc1)
& ? [Xa,Xa1] :
( ~ s_e(Xa,Xc,Xa1,Xc1)
& s_e(Xb,Xc,Xb,Xc1)
& s_e(Xa,Xb,Xa1,Xb)
& s_r(Xa1,Xb,Xc1)
& s_r(Xa,Xb,Xc) ) ) ),
inference(miniscoping,[status(thm)],[f555]) ).
fof(f557,plain,
( sK0_skl != sK1_skl
& sK2_skl = midpoint(sK0_skl,sK1_skl)
& ~ s_e(sK3_skl,sK0_skl,sK4_skl,sK1_skl)
& s_e(sK2_skl,sK0_skl,sK2_skl,sK1_skl)
& s_e(sK3_skl,sK2_skl,sK4_skl,sK2_skl)
& s_r(sK4_skl,sK2_skl,sK1_skl)
& s_r(sK3_skl,sK2_skl,sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl]),skolemize(Xc,sK0_skl),skolemize(Xc1,sK1_skl),skolemize(Xb,sK2_skl),skolemize(Xa,sK3_skl),skolemize(Xa1,sK4_skl)],[f556]) ).
fof(f558,plain,
s_r(sK3_skl,sK2_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f557]) ).
fof(f559,plain,
s_r(sK4_skl,sK2_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f557]) ).
fof(f560,plain,
s_e(sK3_skl,sK2_skl,sK4_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f557]) ).
fof(f562,plain,
~ s_e(sK3_skl,sK0_skl,sK4_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f557]) ).
fof(f563,plain,
sK2_skl = midpoint(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f557]) ).
fof(f620,plain,
( ! [Xa,Xb,Xc] :
( ~ s_e(Xa,Xc,Xa,s(Xb,Xc))
| s_r(Xa,Xb,Xc) )
& ! [Xa,Xb,Xc] :
( s_e(Xa,Xc,Xa,s(Xb,Xc))
| ~ s_r(Xa,Xb,Xc) ) ),
inference(miniscoping,[status(thm)],[f207]) ).
fof(f621,plain,
! [X0,X1,X2] :
( s_e(X0,X2,X0,s(X1,X2))
| ~ s_r(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f620]) ).
fof(f707,plain,
s_m(sK0_skl,sK2_skl,sK1_skl),
inference(paramodulation,[status(thm)],[f563,f467]) ).
fof(f717,plain,
! [X0,X1] :
( ~ s_e(X0,X1,sK4_skl,sK1_skl)
| ~ s_e(X0,X1,sK3_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f562,f214]) ).
fof(f1163,plain,
s_r(sK3_skl,sK2_skl,s(sK2_skl,sK0_skl)),
inference(resolution,[status(thm)],[f411,f558]) ).
fof(f1683,plain,
sK1_skl = s(sK2_skl,sK0_skl),
inference(resolution,[status(thm)],[f375,f707]) ).
fof(f1690,plain,
s_r(sK3_skl,sK2_skl,sK1_skl),
inference(backward_demodulation,[status(thm)],[f1683,f1163]) ).
fof(f1694,plain,
s(sK2_skl,sK1_skl) = sK0_skl,
inference(paramodulation,[status(thm)],[f1683,f376]) ).
fof(f1821,plain,
! [X0] :
( s_e(X0,sK1_skl,sK4_skl,sK1_skl)
| ~ s_e(X0,sK2_skl,sK4_skl,sK2_skl)
| ~ s_r(X0,sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f559,f554]) ).
fof(f2607,plain,
s_e(sK3_skl,sK1_skl,sK3_skl,s(sK2_skl,sK1_skl)),
inference(resolution,[status(thm)],[f1690,f621]) ).
fof(f2616,plain,
s_e(sK3_skl,sK1_skl,sK3_skl,sK0_skl),
inference(forward_demodulation,[status(thm)],[f1694,f2607]) ).
fof(f3094,plain,
( s_e(sK3_skl,sK1_skl,sK4_skl,sK1_skl)
| ~ s_e(sK3_skl,sK2_skl,sK4_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f1821,f1690]) ).
fof(f3099,definition,
( sQ47_spl
<=> s_e(sK3_skl,sK2_skl,sK4_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f3101,plain,
( sQ47_spl
| ~ s_e(sK3_skl,sK2_skl,sK4_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f3099]) ).
fof(f3102,definition,
( sQ48_spl
<=> s_e(sK3_skl,sK1_skl,sK4_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f3103,plain,
( ~ sQ48_spl
| s_e(sK3_skl,sK1_skl,sK4_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f3102]) ).
fof(f3105,plain,
( sQ48_spl
| ~ sQ47_spl ),
inference(split_clause,[status(thm)],[f3094,f3099,f3102]) ).
fof(f3122,plain,
( sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3101,f560]) ).
fof(f3123,plain,
sQ47_spl,
inference(contradiction_clause,[status(thm)],[f3122]) ).
fof(f3462,plain,
~ s_e(sK3_skl,sK1_skl,sK4_skl,sK1_skl),
inference(resolution,[status(thm)],[f2616,f717]) ).
fof(f3463,plain,
( ~ sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3462,f3103]) ).
fof(f3464,plain,
~ sQ48_spl,
inference(contradiction_clause,[status(thm)],[f3463]) ).
fof(f3465,plain,
$false,
inference(sat_refutation,[status(thm)],[f3105,f3123,f3464]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO526+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.42 % Computer : n002.cluster.edu
% 0.16/5.42 % Model : x86_64 x86_64
% 0.16/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.42 % Memory : 8046.5625MB
% 0.16/5.42 % OS : Linux 6.8.0-71-generic
% 0.16/5.43 % CPULimit : 300
% 0.16/5.43 % WCLimit : 300
% 0.16/5.43 % DateTime : Sun Sep 20 17:15:07 UTC 2026
% 0.16/5.43 % CPUTime :
% 0.16/5.47 % Drodi V4.1.1
% 45.35/11.28 % Refutation found
% 45.35/11.28 % SZS status Theorem for theBenchmark: Theorem is valid
% 45.35/11.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.30/11.33 % Elapsed time: 5.883700 seconds
% 4.30/11.33 % CPU time: 46.106904 seconds
% 4.30/11.33 % Total memory used: 207.093 MB
% 4.30/11.33 % Net memory used: 186.881 MB
%------------------------------------------------------------------------------