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G4Plus---1.5.2.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : G4Plus---1.5.2
% Problem  : SEV631+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : g4plus.sh /export/starexec/sandbox/benchmark/theBenchmark.p 300

% Computer : n002.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 12 07:13:49 PM UTC 2026

% Result   : Theorem 31.62s 31.47s
% Output   : Proof 31.62s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEV631+1 : TPTP v9.3.0. Released v9.3.0.
% 0.11/0.13  % Command  : g4plus.sh /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34  % Computer : n002.cluster.edu
% 0.16/0.34  % Model    : x86_64 x86_64
% 0.16/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34  % Memory   : 8042.1875MB
% 0.16/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34  % CPULimit : 300
% 0.16/0.34  % WCLimit  : 300
% 0.16/0.34  % DateTime : Mon May 11 14:05:32 EDT 2026
% 0.16/0.34  % CPUTime  : 
% 31.62/31.47  % SZS status Theorem
% 31.62/31.47  % SZS output start Proof
% 31.62/31.48  
% 31.62/31.48  ===============================================================
% 31.62/31.48  TPTP Problem: _HAMMER_GOAL (conjecture with 3117 axiom(s))
% 31.62/31.48    Axioms: [_HAMMER_COQ_TRUE,_HAMMER_COQ_FALSE,_HAMMER_COQ_TYPE_TYPE,$_case_Coq.Init.Datatypes.list$17865,$_case_Coq.Init.Datatypes.list$35694,$_case_Coq.Init.Datatypes.list$418,$_case_Coq.Init.Datatypes.list$46502,$_case_Coq.Init.Datatypes.list$505,$_case_Coq.Init.Datatypes.nat$120559,$_case_Coq.Init.Datatypes.nat$120581,$_case_Coq.Init.Datatypes.prod$33222,$_case_Coq.Init.Specif.sumbool$15756,$_case_Coq.Numbers.BinNums.Z$120576,$_case_Coq.Numbers.BinNums.Z$37861,$_case_Coq.setoid_ring.Ring_polynom.Pol$12167,$_case_Coq.setoid_ring.Ring_polynom.Pol$12766,$_case_ExtLib.Data.Member.member$17801,$_def_$_let_11_subst_l_24915,$_def_$_let_16_mkpow_28087,$_def_$_let_17_lnum_11934,$_def_$_let_17_mkopp_pow_28088,$_def_$_let_18_mkmult_pow_28089,$_def_$_let_20_lnum_12462,$_def_$_let_var_6_p_28807_28810,$_def_$_let_var_6_p_28809_28811,$_def_$_let_var_var_7_n_15725_15729_15738,$_def_Coq.Arith.PeanoNat.Nat.divide,$_def_Coq.Arith.PeanoNat.Nat.eqf,$_def_Coq.Bool.Bool.Is_true,$_def_Coq.FSets.FSetPositive.PositiveSet.Empty,$_def_Coq.FSets.FSetPositive.PositiveSet.In,$_def_Coq.FSets.FSetPositive.PositiveSet.add,$_def_Coq.FSets.FSetPositive.PositiveSet.elt,$_def_Coq.FSets.FSetPositive.PositiveSet.empty,$_def_Coq.FSets.FSetPositive.PositiveSet.mem,$_def_Coq.FSets.FSetPositive.PositiveSet.rev,$_def_Coq.FSets.FSetPositive.PositiveSet.rev_append,$_def_Coq.FSets.FSetPositive.PositiveSet.t,$_def_Coq.FSets.FSetPositive.PositiveSet.xelements,$_def_Coq.Init.Datatypes.IDProp,$_def_Coq.Init.Datatypes.andb,$_def_Coq.Init.Datatypes.app,$_def_Coq.Init.Datatypes.fst,$_def_Coq.Init.Datatypes.length,$_def_Coq.Init.Datatypes.list_rec,$_def_Coq.Init.Datatypes.list_rect,$_def_Coq.Init.Datatypes.negb,$_def_Coq.Init.Datatypes.orb,$_def_Coq.Init.Datatypes.snd,$_def_Coq.Init.Datatypes.xorb,$_def_Coq.Init.Nat.add,$_def_Coq.Init.Nat.max,$_def_Coq.Init.Nat.min,$_def_Coq.Init.Nat.mul,$_def_Coq.Init.Nat.pow,$_def_Coq.Init.Nat.pred,$_def_Coq.Init.Nat.sub,$_def_Coq.Init.Peano.ge,$_def_Coq.Init.Peano.gt,$_def_Coq.Init.Peano.lt,$_def_Coq.Init.Specif.proj1_sig,$_def_Coq.Init.Specif.projT1,$_def_Coq.Init.Specif.projT2,$_def_Coq.Init.Specif.sumbool_rec,$_def_Coq.Lists.List.ForallPairs,$_def_Coq.Lists.List.In,$_def_Coq.Lists.List.combine,$_def_Coq.Lists.List.concat,$_def_Coq.Lists.List.count_occ,$_def_Coq.Lists.List.existsb,$_def_Coq.Lists.List.filter,$_def_Coq.Lists.List.find,$_def_Coq.Lists.List.firstn,$_def_Coq.Lists.List.flat_map,$_def_Coq.Lists.List.fold_left,$_def_Coq.Lists.List.fold_right,$_def_Coq.Lists.List.forallb,$_def_Coq.Lists.List.hd,$_def_Coq.Lists.List.hd_error,$_def_Coq.Lists.List.incl,$_def_Coq.Lists.List.last,$_def_Coq.Lists.List.lel,$_def_Coq.Lists.List.map,$_def_Coq.Lists.List.nodup,$_def_Coq.Lists.List.nth,$_def_Coq.Lists.List.nth_default,$_def_Coq.Lists.List.nth_error,$_def_Coq.Lists.List.nth_ok,$_def_Coq.Lists.List.partition,$_def_Coq.Lists.List.remove,$_def_Coq.Lists.List.removelast,$_def_Coq.Lists.List.repeat,$_def_Coq.Lists.List.rev,$_def_Coq.Lists.List.rev',$_def_Coq.Lists.List.rev_append,$_def_Coq.Lists.List.seq,$_def_Coq.Lists.List.skipn,$_def_Coq.Lists.List.split,$_def_Coq.Lists.List.tl,$_def_Coq.Lists.SetoidList.equivlistA,$_def_Coq.Lists.SetoidList.inclA,$_def_Coq.Lists.SetoidList.removeA,$_def_Coq.Lists.SetoidList.transpose,$_def_Coq.Lists.SetoidList.transpose2,$_def_Coq.Lists.SetoidList.transpose_restr,$_def_Coq.Lists.SetoidList.transpose_restr2,$_def_Coq.Logic.Decidable.decidable,$_def_Coq.Logic.EqdepFacts.Eq_dep_eq_on,$_def_Coq.Logic.EqdepFacts.Eq_rect_eq_on,$_def_Coq.Logic.EqdepFacts.Streicher_K_on_,$_def_Coq.Logic.EqdepFacts.UIP_on_,$_def_Coq.NArith.BinNat.N.divide,$_def_Coq.NArith.BinNat.N.eqf,$_def_Coq.NArith.BinNat.N.le,$_def_Coq.NArith.BinNat.N.lt,$_def_Coq.NArith.BinNatDef.N.add,$_def_Coq.NArith.BinNatDef.N.div_eucl,$_def_Coq.NArith.BinNatDef.N.eqb,$_def_Coq.NArith.BinNatDef.N.mul,$_def_Coq.NArith.BinNatDef.N.succ,$_def_Coq.NArith.BinNatDef.N.testbit,$_def_Coq.NArith.BinNatDef.N.to_nat,$_def_Coq.PArith.BinPos.Pos.lt,$_def_Coq.PArith.BinPosDef.Pos.add,$_def_Coq.PArith.BinPosDef.Pos.iter,$_def_Coq.PArith.BinPosDef.Pos.pred_double,$_def_Coq.PArith.BinPosDef.Pos.sub,$_def_Coq.PArith.BinPosDef.Pos.succ,$_def_Coq.QArith.QArith_base.Qdiv,$_def_Coq.QArith.QArith_base.Qeq,$_def_Coq.QArith.QArith_base.Qminus,$_def_Coq.QArith.QArith_base.Qmult,$_def_Coq.Reals.Rdefinitions.IZR,$_def_Coq.Reals.Rdefinitions.Rdiv,$_def_Coq.Reals.Rdefinitions.Rge,$_def_Coq.Reals.Rdefinitions.Rgt,$_def_Coq.Reals.Rdefinitions.Rle,$_def_Coq.Reals.Rdefinitions.Rminus,$_def_Coq.Reals.Rpow_def.pow,$_def_Coq.Relations.Relation_Definitions.relation,$_def_Coq.Setoids.Setoid.Setoid_Theory,$_def_Coq.Sets.Relations_1.Transitive,$_def_Coq.Sorting.Sorted.StronglySorted_rect,$_def_Coq.Strings.String.list_ascii_of_string,$_def_Coq.Strings.String.string_of_list_ascii,$_def_Coq.Structures.OrderedTypeEx.N_as_OT.t,$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.t,$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq,$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t,$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% 31.62/31.48  ===============================================================
% 31.62/31.48  
% 31.62/31.48  Combined formula: 3117 axiom(s) => conjecture
% 31.62/31.48  
% 31.62/31.48  % Equality/functions detected -> nanoCoP oracle mode
% 31.62/31.48  nanoCoP : 
% 31.62/31.48  % 23,830,042 inferences, 26.866 CPU in 26.878 seconds (100% CPU, 887006 Lips)
% 31.62/31.48  
% 31.62/31.48  % nanoCoP proof (equality/functions)
% 31.62/31.48  % nanoCoP proof is given at https://g4-mic.vidal-rosset.net/wasm/tinker via nanocop_proves(Your_Formula).
% 31.62/31.48  
% 31.62/31.48  % SZS output end Proof
%------------------------------------------------------------------------------