%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEV678+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 : n007.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 02:33:10 PM UTC 2026
% Result : Theorem 147.14s 147.58s
% Output : CNFRefutation 147.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 9 unt; 5 def)
% Number of atoms : 85 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 83 ( 35 ~; 28 |; 7 &)
% ( 7 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 13 ( 12 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f267,axiom,
( p(cUseAuto_2emyFact)
<=> ! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))
=> cUseAuto_2eP___24a1(V0__x) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1413,axiom,
cCoq_2eNumbers_2eBinNums_2epositive___24t(cCoq_2eNumbers_2eBinNums_2exH),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1688,axiom,
cProp___24t(cUseAuto_2emyFact),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2925,conjecture,
( ! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> cUseAuto_2eP___24a1(V0__x) )
=> p(cUseAuto_2emyFact) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2926,negated_conjecture,
~ ( ! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> cUseAuto_2eP___24a1(V0__x) )
=> p(cUseAuto_2emyFact) ),
inference(negated_conjecture,[status(cth)],[f2925]) ).
fof(f4523,plain,
( p(cUseAuto_2emyFact)
<=> ! [V0__x] :
( cUseAuto_2eP___24a1(V0__x)
| ~ cCoq_2eInit_2ePeano_2ele___24a2(V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(V0__x) ) ),
inference(pre_NNF_transformation,[status(thm)],[f267]) ).
fof(f4524,plain,
( ( ? [V0__x] :
( ~ cUseAuto_2eP___24a1(V0__x)
& cCoq_2eInit_2ePeano_2ele___24a2(V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))
& cCoq_2eInit_2eDatatypes_2enat___24t(V0__x) )
| p(cUseAuto_2emyFact) )
& ( ! [V0__x] :
( cUseAuto_2eP___24a1(V0__x)
| ~ cCoq_2eInit_2ePeano_2ele___24a2(V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(V0__x) )
| ~ p(cUseAuto_2emyFact) ) ),
inference(NNF_transformation,[status(thm)],[f4523]) ).
fof(f4525,plain,
( ( ( ~ cUseAuto_2eP___24a1(sK206_skl)
& cCoq_2eInit_2ePeano_2ele___24a2(sK206_skl,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))
& cCoq_2eInit_2eDatatypes_2enat___24t(sK206_skl) )
| p(cUseAuto_2emyFact) )
& ( ! [V0__x] :
( cUseAuto_2eP___24a1(V0__x)
| ~ cCoq_2eInit_2ePeano_2ele___24a2(V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(V0__x) )
| ~ p(cUseAuto_2emyFact) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK206_skl]),skolemize(V0__x,sK206_skl)],[f4524]) ).
fof(f4527,plain,
( cCoq_2eInit_2eDatatypes_2enat___24t(sK206_skl)
| p(cUseAuto_2emyFact) ),
inference(cnf_transformation,[status(thm)],[f4525]) ).
fof(f4529,plain,
( ~ cUseAuto_2eP___24a1(sK206_skl)
| p(cUseAuto_2emyFact) ),
inference(cnf_transformation,[status(thm)],[f4525]) ).
fof(f9421,plain,
cCoq_2eNumbers_2eBinNums_2epositive___24t(cCoq_2eNumbers_2eBinNums_2exH),
inference(cnf_transformation,[status(thm)],[f1413]) ).
fof(f9696,plain,
cProp___24t(cUseAuto_2emyFact),
inference(cnf_transformation,[status(thm)],[f1688]) ).
fof(f12907,plain,
( ~ p(cUseAuto_2emyFact)
& ! [V0__x] :
( cUseAuto_2eP___24a1(V0__x)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(V0__x) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2926]) ).
fof(f12908,plain,
! [X0] :
( cUseAuto_2eP___24a1(X0)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X0) ),
inference(cnf_transformation,[status(thm)],[f12907]) ).
fof(f12909,plain,
~ p(cUseAuto_2emyFact),
inference(cnf_transformation,[status(thm)],[f12907]) ).
fof(f19011,definition,
( sQ11_spl
<=> p(cUseAuto_2emyFact) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f19012,plain,
( ~ sQ11_spl
| p(cUseAuto_2emyFact) ),
inference(component_clause,[status(thm)],[f19011]) ).
fof(f19018,definition,
( sQ13_spl
<=> cCoq_2eInit_2eDatatypes_2enat___24t(sK206_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f19019,plain,
( ~ sQ13_spl
| cCoq_2eInit_2eDatatypes_2enat___24t(sK206_skl) ),
inference(component_clause,[status(thm)],[f19018]) ).
fof(f19021,plain,
( sQ13_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f4527,f19011,f19018]) ).
fof(f19026,definition,
( sQ15_spl
<=> cUseAuto_2eP___24a1(sK206_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f19028,plain,
( sQ15_spl
| ~ cUseAuto_2eP___24a1(sK206_skl) ),
inference(component_clause,[status(thm)],[f19026]) ).
fof(f19029,plain,
( ~ sQ15_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f4529,f19011,f19026]) ).
fof(f19188,definition,
! [X2] :
( sQ56_spl
<=> ~ cProp___24t(X2) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f19189,plain,
! [X0] :
( ~ sQ56_spl
| ~ cProp___24t(X0) ),
inference(component_clause,[status(thm)],[f19188]) ).
fof(f19263,definition,
! [X2] :
( sQ75_spl
<=> ~ cCoq_2eNumbers_2eBinNums_2epositive___24t(X2) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f19264,plain,
! [X0] :
( ~ sQ75_spl
| ~ cCoq_2eNumbers_2eBinNums_2epositive___24t(X0) ),
inference(component_clause,[status(thm)],[f19263]) ).
fof(f20237,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f19012,f12909]) ).
fof(f20238,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f20237]) ).
fof(f20245,plain,
( ~ sQ56_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f9696,f19189]) ).
fof(f20246,plain,
~ sQ56_spl,
inference(contradiction_clause,[status(thm)],[f20245]) ).
fof(f20486,plain,
( ~ sQ75_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9421,f19264]) ).
fof(f20487,plain,
~ sQ75_spl,
inference(contradiction_clause,[status(thm)],[f20486]) ).
fof(f20745,plain,
( ~ sQ13_spl
| cUseAuto_2eP___24a1(sK206_skl) ),
inference(resolution,[status(thm)],[f19019,f12908]) ).
fof(f20746,plain,
( ~ sQ13_spl
| sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f20745,f19028]) ).
fof(f20747,plain,
( ~ sQ13_spl
| sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f20746]) ).
fof(f20748,plain,
$false,
inference(sat_refutation,[status(thm)],[f19021,f19029,f20238,f20246,f20487,f20747]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEV678+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n007.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 07:33:50 UTC 2026
% 0.17/0.45 % CPUTime :
% 147.00/147.36 % Drodi V4.1.1
% 147.14/147.58 % Refutation found
% 147.14/147.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 147.14/147.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 147.20/147.75 % Elapsed time: 147.274700 seconds
% 147.20/147.75 % CPU time: 148.477182 seconds
% 147.20/147.75 % Total memory used: 2.678 GB
% 147.20/147.75 % Net memory used: 2.674 GB
%------------------------------------------------------------------------------