%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEV606+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 02:33:05 PM UTC 2026
% Result : Theorem 0.43s 1.10s
% Output : CNFRefutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 40 ( 9 unt; 5 def)
% Number of atoms : 123 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 137 ( 54 ~; 48 |; 10 &)
% ( 5 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 6 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 25 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f638,axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f639,axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V2__z))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V2__z)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1138,axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V1__m)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1728,conjecture,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V0__n)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1729,negated_conjecture,
~ ! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V0__n)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1728]) ).
fof(f4397,plain,
! [V0__x] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x))
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x) ),
inference(pre_NNF_transformation,[status(thm)],[f638]) ).
fof(f4398,plain,
! [X0] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X0,X0))
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X0) ),
inference(cnf_transformation,[status(thm)],[f4397]) ).
fof(f4399,plain,
! [V0__x] :
( ! [V1__y] :
( ! [V2__z] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V2__z))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V2__z))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z) )
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y) )
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x) ),
inference(pre_NNF_transformation,[status(thm)],[f639]) ).
fof(f4400,plain,
! [X0,X1,X2] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X0,X2))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X1,X2))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X0,X1))
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X2)
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X1)
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X0) ),
inference(cnf_transformation,[status(thm)],[f4399]) ).
fof(f5639,plain,
! [V0__n] :
( ! [V1__m] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V1__m)))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m) )
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) ),
inference(pre_NNF_transformation,[status(thm)],[f1138]) ).
fof(f5640,plain,
! [X0,X1] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X0,X1))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X0,X0),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X1,X1)))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X1))
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X1)
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X0) ),
inference(cnf_transformation,[status(thm)],[f5639]) ).
fof(f7049,plain,
? [V0__n] :
( ? [V1__m] :
( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V1__m),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V0__n)))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
& cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m) )
& cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) ),
inference(pre_NNF_transformation,[status(thm)],[f1729]) ).
fof(f7050,plain,
( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(sK437_skl,sK436_skl))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(sK437_skl,sK437_skl),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(sK436_skl,sK436_skl)))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,sK437_skl))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,sK436_skl))
& cCoq_2eNumbers_2eBinNums_2eZ___24t(sK437_skl)
& cCoq_2eNumbers_2eBinNums_2eZ___24t(sK436_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK436_skl,sK437_skl]),skolemize(V0__n,sK436_skl),skolemize(V1__m,sK437_skl)],[f7049]) ).
fof(f7051,plain,
cCoq_2eNumbers_2eBinNums_2eZ___24t(sK436_skl),
inference(cnf_transformation,[status(thm)],[f7050]) ).
fof(f7052,plain,
cCoq_2eNumbers_2eBinNums_2eZ___24t(sK437_skl),
inference(cnf_transformation,[status(thm)],[f7050]) ).
fof(f7053,plain,
p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,sK436_skl)),
inference(cnf_transformation,[status(thm)],[f7050]) ).
fof(f7055,plain,
p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(sK437_skl,sK437_skl),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(sK436_skl,sK436_skl))),
inference(cnf_transformation,[status(thm)],[f7050]) ).
fof(f7056,plain,
~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(sK437_skl,sK436_skl)),
inference(cnf_transformation,[status(thm)],[f7050]) ).
fof(f9249,definition,
( sQ83_spl
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(sK437_skl) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f9251,plain,
( sQ83_spl
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(sK437_skl) ),
inference(component_clause,[status(thm)],[f9249]) ).
fof(f9262,definition,
( sQ87_spl
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(sK436_skl) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f9264,plain,
( sQ87_spl
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(sK436_skl) ),
inference(component_clause,[status(thm)],[f9262]) ).
fof(f9275,plain,
( sQ87_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9264,f7051]) ).
fof(f9276,plain,
sQ87_spl,
inference(contradiction_clause,[status(thm)],[f9275]) ).
fof(f9277,plain,
( sQ83_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9251,f7052]) ).
fof(f9278,plain,
sQ83_spl,
inference(contradiction_clause,[status(thm)],[f9277]) ).
fof(f9371,plain,
! [X0] :
( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X0,sK436_skl))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(sK437_skl,X0))
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(sK436_skl)
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X0)
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(sK437_skl) ),
inference(resolution,[status(thm)],[f7056,f4400]) ).
fof(f9372,definition,
! [X0] :
( sQ103_spl
<=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X0,sK436_skl))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(sK437_skl,X0))
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f9373,plain,
! [X0] :
( ~ sQ103_spl
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X0,sK436_skl))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(sK437_skl,X0))
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X0) ),
inference(component_clause,[status(thm)],[f9372]) ).
fof(f9375,plain,
( ~ sQ87_spl
| sQ103_spl
| ~ sQ83_spl ),
inference(split_clause,[status(thm)],[f9371,f9249,f9372,f9262]) ).
fof(f9424,definition,
( sQ110_spl
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,sK436_skl)) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f9426,plain,
( sQ110_spl
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,sK436_skl)) ),
inference(component_clause,[status(thm)],[f9424]) ).
fof(f9435,definition,
( sQ112_spl
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(sK437_skl,sK436_skl)) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f9501,plain,
( ~ sQ103_spl
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(sK437_skl)
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(sK437_skl,sK436_skl))
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(sK437_skl) ),
inference(resolution,[status(thm)],[f9373,f4398]) ).
fof(f9518,plain,
( ~ sQ103_spl
| ~ sQ112_spl
| ~ sQ83_spl ),
inference(split_clause,[status(thm)],[f9501,f9249,f9435,f9372]) ).
fof(f11137,plain,
( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(sK437_skl,sK436_skl))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,sK436_skl))
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(sK436_skl)
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(sK437_skl) ),
inference(resolution,[status(thm)],[f5640,f7055]) ).
fof(f11147,plain,
( sQ112_spl
| ~ sQ110_spl
| ~ sQ87_spl
| ~ sQ83_spl ),
inference(split_clause,[status(thm)],[f11137,f9249,f9262,f9424,f9435]) ).
fof(f11156,plain,
( sQ110_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9426,f7053]) ).
fof(f11157,plain,
sQ110_spl,
inference(contradiction_clause,[status(thm)],[f11156]) ).
fof(f11158,plain,
$false,
inference(sat_refutation,[status(thm)],[f9276,f9278,f9375,f9518,f11147,f11157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV606+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n006.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 : Mon Sep 21 07:29:15 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.29/0.58 % Drodi V4.1.1
% 0.43/1.10 % Refutation found
% 0.43/1.10 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.43/1.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.03/1.15 % Elapsed time: 0.760789 seconds
% 3.03/1.15 % CPU time: 4.287583 seconds
% 3.03/1.15 % Total memory used: 386.403 MB
% 3.03/1.15 % Net memory used: 381.018 MB
%------------------------------------------------------------------------------