TSTP Solution File: SWW677_1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWW677_1 : TPTP v8.2.0. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n007.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 : Mon Jun 24 18:17:59 EDT 2024
% Result : Theorem 0.43s 1.13s
% Output : CNFRefutation 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW677_1 : TPTP v8.2.0. Released v6.4.0.
% 0.11/0.12 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jun 19 05:11:24 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.46 Running TFA theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --no_cores 8 --schedule casc_29_tfa --heuristic_context casc_unsat /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.43/1.13 % SZS status Started for theBenchmark.p
% 0.43/1.13 % SZS status Theorem for theBenchmark.p
% 0.43/1.13
% 0.43/1.13 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.43/1.13
% 0.43/1.13 ------ iProver source info
% 0.43/1.13
% 0.43/1.13 git: date: 2024-06-12 09:56:46 +0000
% 0.43/1.13 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 0.43/1.13 git: non_committed_changes: false
% 0.43/1.13
% 0.43/1.13 ------ Parsing...
% 0.43/1.13 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.43/1.13
% 0.43/1.13 ------ Preprocessing... sup_sim: 5 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 0.43/1.13
% 0.43/1.13 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.43/1.13
% 0.43/1.13 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.43/1.13 ------ Proving...
% 0.43/1.13 ------ Problem Properties
% 0.43/1.13
% 0.43/1.13
% 0.43/1.13 clauses 44
% 0.43/1.13 conjectures 4
% 0.43/1.13 EPR 9
% 0.43/1.13 Horn 36
% 0.43/1.13 unary 28
% 0.43/1.13 binary 11
% 0.43/1.13 lits 67
% 0.43/1.13 lits eq 27
% 0.43/1.13 fd_pure 0
% 0.43/1.13 fd_pseudo 0
% 0.43/1.13 fd_cond 0
% 0.43/1.13 fd_pseudo_cond 5
% 0.43/1.13 AC symbols 2
% 0.43/1.13
% 0.43/1.13 ------ Input Options Time Limit: Unbounded
% 0.43/1.13
% 0.43/1.13
% 0.43/1.13 ------
% 0.43/1.13 Current options:
% 0.43/1.13 ------
% 0.43/1.13
% 0.43/1.13
% 0.43/1.13
% 0.43/1.13
% 0.43/1.13 ------ Proving...
% 0.43/1.13
% 0.43/1.13
% 0.43/1.13 % SZS status Theorem for theBenchmark.p
% 0.43/1.13
% 0.43/1.13 % SZS output start CNFRefutation for theBenchmark.p
% 0.43/1.13
% 0.43/1.13 tff(f5,axiom,(
% 0.43/1.13 ! [X0 : $int,X5 : $int] : (($greater($product(2,$sum(X5,1)),X0) & $lesseq($product(2,X5),X0)) <=> div2(X0) = X5)),
% 0.43/1.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_004)).
% 0.43/1.13
% 0.43/1.13 tff(f8,conjecture,(
% 0.43/1.13 ! [X6 : $int,X7 : $int,X0 : 'Array[Int,Int]',X2 : $int] : ((sorted(X0,0,$difference(length(X0),1)) & $less(X7,length(X0)) & $lesseq(0,X6)) => ((~$greater(X6,X7) => ? [X8 : $int] : (('select:(Array[Int,Int]*Int)>Int'(X0,X8) != X2 => ((~$less('select:(Array[Int,Int]*Int)>Int'(X0,X8),X2) => ? [X10 : $int] : (sorted(X0,0,$difference(length(X0),1)) & $less(X10,length(X0)) & $lesseq(0,X6) & $difference(X8,1) = X10)) & ($less('select:(Array[Int,Int]*Int)>Int'(X0,X8),X2) => ? [X9 : $int] : (sorted(X0,0,$difference(length(X0),1)) & $less(X7,length(X0)) & $lesseq(0,X9) & $sum(X8,1) = X9)))) & ('select:(Array[Int,Int]*Int)>Int'(X0,X8) = X2 => $true) & div2($sum(X6,X7)) = X8)) & ($greater(X6,X7) => $true)))),
% 0.43/1.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_007)).
% 0.43/1.13
% 0.43/1.13 tff(f9,negated_conjecture,(
% 0.43/1.13 ~! [X6 : $int,X7 : $int,X0 : 'Array[Int,Int]',X2 : $int] : ((sorted(X0,0,$difference(length(X0),1)) & $less(X7,length(X0)) & $lesseq(0,X6)) => ((~$greater(X6,X7) => ? [X8 : $int] : (('select:(Array[Int,Int]*Int)>Int'(X0,X8) != X2 => ((~$less('select:(Array[Int,Int]*Int)>Int'(X0,X8),X2) => ? [X10 : $int] : (sorted(X0,0,$difference(length(X0),1)) & $less(X10,length(X0)) & $lesseq(0,X6) & $difference(X8,1) = X10)) & ($less('select:(Array[Int,Int]*Int)>Int'(X0,X8),X2) => ? [X9 : $int] : (sorted(X0,0,$difference(length(X0),1)) & $less(X7,length(X0)) & $lesseq(0,X9) & $sum(X8,1) = X9)))) & ('select:(Array[Int,Int]*Int)>Int'(X0,X8) = X2 => $true) & div2($sum(X6,X7)) = X8)) & ($greater(X6,X7) => $true)))),
% 0.43/1.13 inference(negated_conjecture,[],[f8])).
% 0.43/1.13
% 0.43/1.13 tff(f10,plain,(
% 0.43/1.13 ! [X0 : $int,X5 : $int] : (($less(X0,$product(2,$sum(X5,1))) & ~$less(X0,$product(2,X5))) <=> div2(X0) = X5)),
% 0.43/1.13 inference(theory_normalization,[],[f5])).
% 0.43/1.13
% 0.43/1.13 tff(f13,plain,(
% 0.43/1.13 ~! [X6 : $int,X7 : $int,X0 : 'Array[Int,Int]',X2 : $int] : ((sorted(X0,0,$sum(length(X0),$uminus(1))) & $less(X7,length(X0)) & ~$less(X6,0)) => ((~$less(X7,X6) => ? [X8 : $int] : (('select:(Array[Int,Int]*Int)>Int'(X0,X8) != X2 => ((~$less('select:(Array[Int,Int]*Int)>Int'(X0,X8),X2) => ? [X10 : $int] : (sorted(X0,0,$sum(length(X0),$uminus(1))) & $less(X10,length(X0)) & ~$less(X6,0) & $sum(X8,$uminus(1)) = X10)) & ($less('select:(Array[Int,Int]*Int)>Int'(X0,X8),X2) => ? [X9 : $int] : (sorted(X0,0,$sum(length(X0),$uminus(1))) & $less(X7,length(X0)) & ~$less(X9,0) & $sum(X8,1) = X9)))) & ('select:(Array[Int,Int]*Int)>Int'(X0,X8) = X2 => $true) & div2($sum(X6,X7)) = X8)) & ($less(X7,X6) => $true)))),
% 0.43/1.13 inference(theory_normalization,[],[f9])).
% 0.43/1.13
% 0.43/1.13 tff(f14,plain,(
% 0.43/1.13 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.43/1.13 introduced(theory_axiom_138,[])).
% 0.43/1.13
% 0.43/1.13 tff(f15,plain,(
% 0.43/1.13 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 0.43/1.13 introduced(theory_axiom_139,[])).
% 0.43/1.13
% 0.43/1.13 tff(f18,plain,(
% 0.43/1.13 ( ! [X0 : $int] : (0 = $sum(X0,$uminus(X0))) )),
% 0.43/1.13 introduced(theory_axiom_143,[])).
% 0.43/1.13
% 0.43/1.13 tff(f20,plain,(
% 0.43/1.13 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X0,X1) | ~$less(X1,X2) | $less(X0,X2)) )),
% 0.43/1.13 introduced(theory_axiom_146,[])).
% 0.43/1.13
% 0.43/1.13 tff(f21,plain,(
% 0.43/1.13 ( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | $less(X1,X0) | X0 = X1) )),
% 0.43/1.13 introduced(theory_axiom_147,[])).
% 0.43/1.13
% 0.43/1.13 tff(f23,plain,(
% 0.43/1.13 ( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | $less(X1,$sum(X0,1))) )),
% 0.43/1.13 introduced(theory_axiom_150,[])).
% 0.43/1.13
% 0.43/1.13 tff(f25,plain,(
% 0.43/1.13 ( ! [X0 : $int,X1 : $int] : ($product(X0,X1) = $product(X1,X0)) )),
% 0.43/1.13 introduced(theory_axiom_138,[])).
% 0.43/1.13
% 0.43/1.13 tff(f26,plain,(
% 0.43/1.13 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($product(X0,$product(X1,X2)) = $product($product(X0,X1),X2)) )),
% 0.43/1.13 introduced(theory_axiom_139,[])).
% 0.43/1.13
% 0.43/1.13 tff(f27,plain,(
% 0.43/1.13 ( ! [X0 : $int] : ($product(X0,1) = X0) )),
% 0.43/1.13 introduced(theory_axiom_140,[])).
% 0.43/1.13
% 0.43/1.13 tff(f29,plain,(
% 0.43/1.13 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2))) )),
% 0.43/1.13 introduced(theory_axiom_153,[])).
% 0.43/1.13
% 0.43/1.13 tff(f35,plain,(
% 0.43/1.13 ! [X0 : $int,X1 : $int] : (($less(X0,$product(2,$sum(X1,1))) & ~$less(X0,$product(2,X1))) <=> div2(X0) = X1)),
% 0.43/1.13 inference(rectify,[],[f10])).
% 0.43/1.13
% 0.43/1.13 tff(f37,plain,(
% 0.43/1.13 ~! [X0 : $int,X1 : $int,X2 : 'Array[Int,Int]',X3 : $int] : ((sorted(X2,0,$sum(length(X2),$uminus(1))) & $less(X1,length(X2)) & ~$less(X0,0)) => ((~$less(X1,X0) => ? [X4 : $int] : (('select:(Array[Int,Int]*Int)>Int'(X2,X4) != X3 => ((~$less('select:(Array[Int,Int]*Int)>Int'(X2,X4),X3) => ? [X5 : $int] : (sorted(X2,0,$sum(length(X2),$uminus(1))) & $less(X5,length(X2)) & ~$less(X0,0) & $sum(X4,$uminus(1)) = X5)) & ($less('select:(Array[Int,Int]*Int)>Int'(X2,X4),X3) => ? [X6 : $int] : (sorted(X2,0,$sum(length(X2),$uminus(1))) & $less(X1,length(X2)) & ~$less(X6,0) & $sum(X4,1) = X6)))) & ('select:(Array[Int,Int]*Int)>Int'(X2,X4) = X3 => $true) & div2($sum(X0,X1)) = X4)) & ($less(X1,X0) => $true)))),
% 0.43/1.13 inference(rectify,[],[f13])).
% 0.43/1.13
% 0.43/1.13 tff(f38,plain,(
% 0.43/1.13 ~! [X0 : $int,X1 : $int,X2 : 'Array[Int,Int]',X3 : $int] : ((sorted(X2,0,$sum(length(X2),$uminus(1))) & $less(X1,length(X2)) & ~$less(X0,0)) => (~$less(X1,X0) => ? [X4 : $int] : (('select:(Array[Int,Int]*Int)>Int'(X2,X4) != X3 => ((~$less('select:(Array[Int,Int]*Int)>Int'(X2,X4),X3) => ? [X5 : $int] : (sorted(X2,0,$sum(length(X2),$uminus(1))) & $less(X5,length(X2)) & ~$less(X0,0) & $sum(X4,$uminus(1)) = X5)) & ($less('select:(Array[Int,Int]*Int)>Int'(X2,X4),X3) => ? [X6 : $int] : (sorted(X2,0,$sum(length(X2),$uminus(1))) & $less(X1,length(X2)) & ~$less(X6,0) & $sum(X4,1) = X6)))) & div2($sum(X0,X1)) = X4)))),
% 0.43/1.13 inference(true_and_false_elimination,[],[f37])).
% 0.43/1.13
% 0.43/1.13 tff(f43,plain,(
% 0.43/1.13 ? [X0 : $int,X1 : $int,X2 : 'Array[Int,Int]',X3 : $int] : ((! [X4 : $int] : ((((! [X5 : $int] : (~sorted(X2,0,$sum(length(X2),$uminus(1))) | ~$less(X5,length(X2)) | $less(X0,0) | $sum(X4,$uminus(1)) != X5) & ~$less('select:(Array[Int,Int]*Int)>Int'(X2,X4),X3)) | (! [X6 : $int] : (~sorted(X2,0,$sum(length(X2),$uminus(1))) | ~$less(X1,length(X2)) | $less(X6,0) | $sum(X4,1) != X6) & $less('select:(Array[Int,Int]*Int)>Int'(X2,X4),X3))) & 'select:(Array[Int,Int]*Int)>Int'(X2,X4) != X3) | div2($sum(X0,X1)) != X4) & ~$less(X1,X0)) & (sorted(X2,0,$sum(length(X2),$uminus(1))) & $less(X1,length(X2)) & ~$less(X0,0)))),
% 0.43/1.13 inference(ennf_transformation,[],[f38])).
% 0.43/1.13
% 0.43/1.13 tff(f44,plain,(
% 0.43/1.13 ? [X0 : $int,X1 : $int,X2 : 'Array[Int,Int]',X3 : $int] : (! [X4 : $int] : ((((! [X5 : $int] : (~sorted(X2,0,$sum(length(X2),$uminus(1))) | ~$less(X5,length(X2)) | $less(X0,0) | $sum(X4,$uminus(1)) != X5) & ~$less('select:(Array[Int,Int]*Int)>Int'(X2,X4),X3)) | (! [X6 : $int] : (~sorted(X2,0,$sum(length(X2),$uminus(1))) | ~$less(X1,length(X2)) | $less(X6,0) | $sum(X4,1) != X6) & $less('select:(Array[Int,Int]*Int)>Int'(X2,X4),X3))) & 'select:(Array[Int,Int]*Int)>Int'(X2,X4) != X3) | div2($sum(X0,X1)) != X4) & ~$less(X1,X0) & sorted(X2,0,$sum(length(X2),$uminus(1))) & $less(X1,length(X2)) & ~$less(X0,0))),
% 0.43/1.13 inference(flattening,[],[f43])).
% 0.43/1.13
% 0.43/1.13 tff(f47,plain,(
% 0.43/1.13 ! [X0 : $int,X1 : $int] : ((($less(X0,$product(2,$sum(X1,1))) & ~$less(X0,$product(2,X1))) | div2(X0) != X1) & (div2(X0) = X1 | (~$less(X0,$product(2,$sum(X1,1))) | $less(X0,$product(2,X1)))))),
% 0.43/1.13 inference(nnf_transformation,[],[f35])).
% 0.43/1.13
% 0.43/1.13 tff(f48,plain,(
% 0.43/1.13 ! [X0 : $int,X1 : $int] : ((($less(X0,$product(2,$sum(X1,1))) & ~$less(X0,$product(2,X1))) | div2(X0) != X1) & (div2(X0) = X1 | ~$less(X0,$product(2,$sum(X1,1))) | $less(X0,$product(2,X1))))),
% 0.43/1.13 inference(flattening,[],[f47])).
% 0.43/1.13
% 0.43/1.13 tff(f53,plain,(
% 0.43/1.13 ? [X0 : $int,X1 : $int,X2 : 'Array[Int,Int]',X3 : $int] : (! [X4 : $int] : ((((! [X5 : $int] : (~sorted(X2,0,$sum(length(X2),$uminus(1))) | ~$less(X5,length(X2)) | $less(X0,0) | $sum(X4,$uminus(1)) != X5) & ~$less('select:(Array[Int,Int]*Int)>Int'(X2,X4),X3)) | (! [X6 : $int] : (~sorted(X2,0,$sum(length(X2),$uminus(1))) | ~$less(X1,length(X2)) | $less(X6,0) | $sum(X4,1) != X6) & $less('select:(Array[Int,Int]*Int)>Int'(X2,X4),X3))) & 'select:(Array[Int,Int]*Int)>Int'(X2,X4) != X3) | div2($sum(X0,X1)) != X4) & ~$less(X1,X0) & sorted(X2,0,$sum(length(X2),$uminus(1))) & $less(X1,length(X2)) & ~$less(X0,0)) => (! [X4 : $int] : ((((! [X5 : $int] : (~sorted(sK5,0,$sum(length(sK5),$uminus(1))) | ~$less(X5,length(sK5)) | $less(sK3,0) | $sum(X4,$uminus(1)) != X5) & ~$less('select:(Array[Int,Int]*Int)>Int'(sK5,X4),sK6)) | (! [X6 : $int] : (~sorted(sK5,0,$sum(length(sK5),$uminus(1))) | ~$less(sK4,length(sK5)) | $less(X6,0) | $sum(X4,1) != X6) & $less('select:(Array[Int,Int]*Int)>Int'(sK5,X4),sK6))) & sK6 != 'select:(Array[Int,Int]*Int)>Int'(sK5,X4)) | div2($sum(sK3,sK4)) != X4) & ~$less(sK4,sK3) & sorted(sK5,0,$sum(length(sK5),$uminus(1))) & $less(sK4,length(sK5)) & ~$less(sK3,0))),
% 0.43/1.13 introduced(choice_axiom,[])).
% 0.43/1.13
% 0.43/1.13 tff(f54,plain,(
% 0.43/1.13 ! [X4 : $int] : ((((! [X5 : $int] : (~sorted(sK5,0,$sum(length(sK5),$uminus(1))) | ~$less(X5,length(sK5)) | $less(sK3,0) | $sum(X4,$uminus(1)) != X5) & ~$less('select:(Array[Int,Int]*Int)>Int'(sK5,X4),sK6)) | (! [X6 : $int] : (~sorted(sK5,0,$sum(length(sK5),$uminus(1))) | ~$less(sK4,length(sK5)) | $less(X6,0) | $sum(X4,1) != X6) & $less('select:(Array[Int,Int]*Int)>Int'(sK5,X4),sK6))) & sK6 != 'select:(Array[Int,Int]*Int)>Int'(sK5,X4)) | div2($sum(sK3,sK4)) != X4) & ~$less(sK4,sK3) & sorted(sK5,0,$sum(length(sK5),$uminus(1))) & $less(sK4,length(sK5)) & ~$less(sK3,0)),
% 0.43/1.13 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f44,f53])).
% 0.43/1.13
% 0.43/1.13 tff(f60,plain,(
% 0.43/1.13 ( ! [X0 : $int,X1 : $int] : (~$less(X0,$product(2,X1)) | div2(X0) != X1) )),
% 0.43/1.13 inference(cnf_transformation,[],[f48])).
% 0.43/1.13
% 0.43/1.13 tff(f61,plain,(
% 0.43/1.13 ( ! [X0 : $int,X1 : $int] : ($less(X0,$product(2,$sum(X1,1))) | div2(X0) != X1) )),
% 0.43/1.13 inference(cnf_transformation,[],[f48])).
% 0.43/1.13
% 0.43/1.13 tff(f68,plain,(
% 0.43/1.13 ~$less(sK3,0)),
% 0.43/1.13 inference(cnf_transformation,[],[f54])).
% 0.43/1.13
% 0.43/1.13 tff(f69,plain,(
% 0.43/1.13 $less(sK4,length(sK5))),
% 0.43/1.13 inference(cnf_transformation,[],[f54])).
% 0.43/1.13
% 0.43/1.13 tff(f70,plain,(
% 0.43/1.13 sorted(sK5,0,$sum(length(sK5),$uminus(1)))),
% 0.43/1.13 inference(cnf_transformation,[],[f54])).
% 0.43/1.13
% 0.43/1.13 tff(f71,plain,(
% 0.43/1.13 ~$less(sK4,sK3)),
% 0.43/1.13 inference(cnf_transformation,[],[f54])).
% 0.43/1.13
% 0.43/1.13 tff(f78,plain,(
% 0.43/1.13 ( ! [X0 : $int] : ($less(X0,$product(2,$sum(div2(X0),1)))) )),
% 0.43/1.13 inference(equality_resolution,[],[f61])).
% 0.43/1.13
% 0.43/1.13 tff(f79,plain,(
% 0.43/1.13 ( ! [X0 : $int] : (~$less(X0,$product(2,div2(X0)))) )),
% 0.43/1.13 inference(equality_resolution,[],[f60])).
% 0.43/1.13
% 0.43/1.13 cnf(c_51,plain,
% 0.43/1.13 ($sum_int($product_int(X0_3,X1_3),$product_int(X0_3,X2_3)) = $product_int(X0_3,$sum_int(X1_3,X2_3))),
% 0.43/1.13 inference(cnf_transformation,[],[f29])).
% 0.43/1.13
% 0.43/1.13 cnf(c_53,plain,
% 0.43/1.13 ($product_int(X0_3,1) = X0_3),
% 0.43/1.13 inference(cnf_transformation,[],[f27])).
% 0.43/1.13
% 0.43/1.13 cnf(c_54,plain,
% 0.43/1.13 ($product_int($product_int(X0_3,X1_3),X2_3) = $product_int(X0_3,$product_int(X1_3,X2_3))),
% 0.43/1.13 inference(cnf_transformation,[],[f26])).
% 0.43/1.13
% 0.43/1.13 cnf(c_55,plain,
% 0.43/1.13 ($product_int(X0_3,X1_3) = $product_int(X1_3,X0_3)),
% 0.43/1.13 inference(cnf_transformation,[],[f25])).
% 0.43/1.13
% 0.43/1.13 cnf(c_57,plain,
% 0.43/1.13 ($less_int(X0_3,$sum_int(X1_3,1))|$less_int(X1_3,X0_3)),
% 0.43/1.13 inference(cnf_transformation,[],[f23])).
% 0.43/1.13
% 0.43/1.13 cnf(c_59,plain,
% 0.43/1.13 (X0_3 = X1_3|$less_int(X0_3,X1_3)|$less_int(X1_3,X0_3)),
% 0.43/1.13 inference(cnf_transformation,[],[f21])).
% 0.43/1.13
% 0.43/1.13 cnf(c_60,plain,
% 0.43/1.13 (~$less_int(X0_3,X1_3)|~$less_int(X1_3,X2_3)|$less_int(X0_3,X2_3)),
% 0.43/1.13 inference(cnf_transformation,[],[f20])).
% 0.43/1.13
% 0.43/1.13 cnf(c_62,plain,
% 0.43/1.13 ($sum_int(X0_3,$uminus_int(X0_3)) = 0),
% 0.43/1.13 inference(cnf_transformation,[],[f18])).
% 0.43/1.13
% 0.43/1.13 cnf(c_65,plain,
% 0.43/1.13 ($sum_int($sum_int(X0_3,X1_3),X2_3) = $sum_int(X0_3,$sum_int(X1_3,X2_3))),
% 0.43/1.13 inference(cnf_transformation,[],[f15])).
% 0.43/1.13
% 0.43/1.13 cnf(c_66,plain,
% 0.43/1.13 ($sum_int(X0_3,X1_3) = $sum_int(X1_3,X0_3)),
% 0.43/1.13 inference(cnf_transformation,[],[f14])).
% 0.43/1.13
% 0.43/1.13 cnf(c_71,plain,
% 0.43/1.13 ($less_int(X0_3,$product_int(2,$sum_int(div2(X0_3),1)))),
% 0.43/1.13 inference(cnf_transformation,[],[f78])).
% 0.43/1.13
% 0.43/1.13 cnf(c_72,plain,
% 0.43/1.13 (~$less_int(X0_3,$product_int(2,div2(X0_3)))),
% 0.43/1.13 inference(cnf_transformation,[],[f79])).
% 0.43/1.13
% 0.43/1.13 cnf(c_80,negated_conjecture,
% 0.43/1.13 (~$less_int($sum_int(div2($sum_int(sK3,sK4)),$uminus_int(1)),length(sK5))|
% 0.43/1.13 ~sorted(sK5,0,$sum_int(length(sK5),$uminus_int(1)))|~$less_int(sK4,length(sK5))|
% 0.43/1.13 $less_int($sum_int(div2($sum_int(sK3,sK4)),1),0)|$less_int(sK3,0)),
% 0.43/1.13 inference(cnf_transformation,[],[f120])).
% 0.43/1.13
% 0.43/1.13 cnf(c_84,negated_conjecture,
% 0.43/1.13 (~$less_int(sK4,sK3)),
% 0.43/1.13 inference(cnf_transformation,[],[f71])).
% 0.43/1.13
% 0.43/1.13 cnf(c_85,negated_conjecture,
% 0.43/1.13 (sorted(sK5,0,$sum_int(length(sK5),$uminus_int(1)))),
% 0.43/1.13 inference(cnf_transformation,[],[f70])).
% 0.43/1.13
% 0.43/1.13 cnf(c_86,negated_conjecture,
% 0.43/1.13 ($less_int(sK4,length(sK5))),
% 0.43/1.13 inference(cnf_transformation,[],[f69])).
% 0.43/1.13
% 0.43/1.13 cnf(c_87,negated_conjecture,
% 0.43/1.13 (~$less_int(sK3,0)),
% 0.43/1.13 inference(cnf_transformation,[],[f68])).
% 0.43/1.13
% 0.43/1.13 cnf(c_121,plain,
% 0.43/1.13 ($less_int($sum_int(div2($sum_int(sK3,sK4)),1),0)|~$less_int($sum_int(div2($sum_int(sK3,sK4)),$uminus_int(1)),length(sK5))),
% 0.43/1.13 inference(global_subsumption_just,
% 0.43/1.13 [status(thm)],
% 0.43/1.13 [c_80,c_87,c_86,c_85,c_80])).
% 0.43/1.13
% 0.43/1.13 cnf(c_122,negated_conjecture,
% 0.43/1.13 (~$less_int($sum_int(div2($sum_int(sK3,sK4)),$uminus_int(1)),length(sK5))|
% 0.43/1.13 $less_int($sum_int(div2($sum_int(sK3,sK4)),1),0)),
% 0.43/1.13 inference(renaming,[status(thm)],[c_121])).
% 0.43/1.13
% 0.43/1.13 cnf(c_123,plain,
% 0.43/1.13 ($less_int(X0_3,$product_int(2,$sum_int(1,div2(X0_3))))),
% 0.43/1.13 inference(theory_normalisation,[status(thm)],[c_71,c_54,c_55,c_65,c_66])).
% 0.43/1.13
% 0.43/1.13 cnf(c_127,negated_conjecture,
% 0.43/1.13 (~$less_int($sum_int($uminus_int(1),div2($sum_int(sK3,sK4))),length(sK5))|
% 0.43/1.13 $less_int($sum_int(1,div2($sum_int(sK3,sK4))),0)),
% 0.43/1.13 inference(theory_normalisation,[status(thm)],[c_122,c_54,c_55,c_65,c_66])).
% 0.43/1.13
% 0.43/1.13 cnf(c_166,plain,
% 0.43/1.13 (~$less_int($sum_int($uminus_int(1),div2($sum_int(sK3,sK4))),length(sK5))|
% 0.43/1.13 $less_int($sum_int(1,div2($sum_int(sK3,sK4))),0)),
% 0.43/1.13 inference(prop_impl_just,[status(thm)],[c_127])).
% 0.43/1.13
% 0.43/1.13 cnf(c_424,plain,
% 0.43/1.13 (~$less_int($sum_int(-1,div2($sum_int(sK3,sK4))),length(sK5))|$less_int(div2($sum_int(sK3,sK4)),-1)),
% 0.43/1.13 inference(smt_theory_normalisation,[status(thm)],[c_166])).
% 0.43/1.13
% 0.43/1.13 cnf(c_597,plain,
% 0.43/1.13 ($less_int(div2($sum_int(sK3,sK4)),-1)|~$less_int($sum_int(-1,div2($sum_int(sK3,sK4))),length(sK5))),
% 0.43/1.13 inference(prop_impl_just,[status(thm)],[c_424])).
% 0.43/1.13
% 0.43/1.13 cnf(c_598,plain,
% 0.43/1.13 (~$less_int($sum_int(-1,div2($sum_int(sK3,sK4))),length(sK5))|$less_int(div2($sum_int(sK3,sK4)),-1)),
% 0.43/1.13 inference(renaming,[status(thm)],[c_597])).
% 0.43/1.13
% 0.43/1.13 cnf(c_983,plain,(length(sK5) = sP0_iProver_def),definition).
% 0.43/1.13
% 0.43/1.13 cnf(c_984,plain,($sum_int(sK3,sK4) = sP1_iProver_def),definition).
% 0.43/1.13
% 0.43/1.13 cnf(c_985,plain,(div2(sP1_iProver_def) = sP2_iProver_def),definition).
% 0.43/1.13
% 0.43/1.13 cnf(c_987,negated_conjecture,
% 0.43/1.13 (~$less_int(sK3,0)),
% 0.43/1.13 inference(demodulation,[status(thm)],[c_87])).
% 0.43/1.13
% 0.43/1.13 cnf(c_988,negated_conjecture,
% 0.43/1.13 ($less_int(sK4,sP0_iProver_def)),
% 0.43/1.13 inference(demodulation,[status(thm)],[c_86,c_983])).
% 0.43/1.13
% 0.43/1.13 cnf(c_989,negated_conjecture,
% 0.43/1.13 (~$less_int(sK4,sK3)),
% 0.43/1.13 inference(demodulation,[status(thm)],[c_84])).
% 0.43/1.13
% 0.43/1.13 cnf(c_992,plain,(X0_3 = X0_3),theory(equality)).
% 0.43/1.13
% 0.43/1.13 cnf(c_999,plain,
% 0.43/1.13 (X0_3 != X1_3|X2_3 != X3_3|~$less_int(X1_3,X3_3)|$less_int(X0_3,X2_3)),
% 0.43/1.13 theory(equality)).
% 0.43/1.13
% 0.43/1.13 cnf(c_1687,plain,
% 0.43/1.13 (~$less_int(sP1_iProver_def,$product_int(2,sP2_iProver_def))),
% 0.43/1.13 inference(superposition,[status(thm)],[c_985,c_72])).
% 0.43/1.13
% 0.43/1.13 cnf(c_1688,plain,
% 0.43/1.13 (~$less_int(sP1_iProver_def,$product_int(sP2_iProver_def,2))),
% 0.43/1.13 inference(theory_normalisation,
% 0.43/1.13 [status(thm)],
% 0.43/1.13 [c_1687,c_65,c_66,c_54,c_55])).
% 0.43/1.13
% 0.43/1.13 cnf(c_1723,plain,
% 0.43/1.13 ($less_int(X0_3,$sum_int(1,X1_3))|$less_int(X1_3,X0_3)),
% 0.43/1.13 inference(superposition,[status(thm)],[c_66,c_57])).
% 0.43/1.13
% 0.43/1.13 cnf(c_1728,plain,
% 0.43/1.13 ($less_int(sP1_iProver_def,$product_int(2,$sum_int(1,sP2_iProver_def)))),
% 0.43/1.13 inference(superposition,[status(thm)],[c_985,c_123])).
% 0.43/1.13
% 0.43/1.13 cnf(c_1729,plain,
% 0.43/1.13 ($less_int(sP1_iProver_def,$product_int(2,$sum_int(sP2_iProver_def,1)))),
% 0.43/1.13 inference(theory_normalisation,
% 0.43/1.13 [status(thm)],
% 0.43/1.13 [c_1728,c_65,c_66,c_54,c_55])).
% 0.43/1.13
% 0.43/1.13 cnf(c_1770,plain,
% 0.43/1.13 ($less_int($uminus_int(1),X0_3)|$less_int(X0_3,0)),
% 0.43/1.13 inference(superposition,[status(thm)],[c_62,c_1723])).
% 0.43/1.13
% 0.43/1.13 cnf(c_1781,plain,
% 0.43/1.13 ($less_int(X0_3,0)|$less_int(-1,X0_3)),
% 0.43/1.13 inference(smt_theory_normalisation,[status(thm)],[c_1770])).
% 0.43/1.13
% 0.43/1.13 cnf(c_1791,plain,
% 0.43/1.13 ($less_int(-1,sK3)),
% 0.43/1.13 inference(superposition,[status(thm)],[c_1781,c_987])).
% 0.43/1.13
% 0.43/1.13 cnf(c_1890,plain,
% 0.43/1.13 (~$less_int(sP0_iProver_def,X0_3)|$less_int(sK4,X0_3)),
% 0.43/1.13 inference(superposition,[status(thm)],[c_988,c_60])).
% 0.43/1.13
% 0.43/1.13 cnf(c_2020,plain,
% 0.43/1.13 (X0_3 = sP0_iProver_def|$less_int(X0_3,sP0_iProver_def)|$less_int(sK4,X0_3)),
% 0.43/1.13 inference(superposition,[status(thm)],[c_59,c_1890])).
% 0.43/1.13
% 0.43/1.13 cnf(c_2096,plain,
% 0.43/1.13 (X0_3 != sK4|X1_3 != sP0_iProver_def|~$less_int(sK4,sP0_iProver_def)|
% 0.43/1.13 $less_int(X0_3,X1_3)),
% 0.43/1.13 inference(instantiation,[status(thm)],[c_999])).
% 0.43/1.13
% 0.43/1.13 cnf(c_2261,plain,
% 0.43/1.13 (X0_3 != sP0_iProver_def|sK4 != sK4|~$less_int(sK4,sP0_iProver_def)|
% 0.43/1.13 $less_int(sK4,X0_3)),
% 0.43/1.13 inference(instantiation,[status(thm)],[c_2096])).
% 0.43/1.13
% 0.43/1.13 cnf(c_2262,plain,(sK4 = sK4),inference(instantiation,[status(thm)],[c_992])).
% 0.43/1.13
% 0.43/1.13 cnf(c_2281,plain,
% 0.43/1.13 ($sum_int(sK3,$sum_int(sK4,X0_3)) = $sum_int(sP1_iProver_def,X0_3)),
% 0.43/1.13 inference(superposition,[status(thm)],[c_984,c_65])).
% 0.43/1.13
% 0.43/1.13 cnf(c_2328,plain,
% 0.43/1.13 ($less_int(X0_3,sP0_iProver_def)|$less_int(sK4,X0_3)),
% 0.43/1.13 inference(global_subsumption_just,
% 0.43/1.13 [status(thm)],
% 0.43/1.13 [c_2020,c_988,c_2020,c_2261,c_2262])).
% 0.43/1.13
% 0.43/1.13 cnf(c_2340,plain,
% 0.43/1.13 ($less_int(sK3,sP0_iProver_def)),
% 0.43/1.13 inference(superposition,[status(thm)],[c_2328,c_989])).
% 0.43/1.13
% 0.43/1.13 cnf(c_2592,plain,
% 0.43/1.13 ($sum_int($product_int(X0_3,X1_3),X0_3) = $product_int(X0_3,$sum_int(X1_3,1))),
% 0.43/1.13 inference(superposition,[status(thm)],[c_53,c_51])).
% 0.43/1.13
% 0.43/1.13 cnf(c_2606,plain,
% 0.43/1.13 ($sum_int(X0_3,$product_int(X0_3,X1_3)) = $product_int(X0_3,$sum_int(X1_3,1))),
% 0.43/1.13 inference(theory_normalisation,
% 0.43/1.13 [status(thm)],
% 0.43/1.13 [c_2592,c_65,c_66,c_54,c_55])).
% 0.43/1.13
% 0.43/1.13 cnf(c_2612,plain,
% 0.43/1.13 ($less_int(sP1_iProver_def,$sum_int(2,$product_int(2,sP2_iProver_def)))),
% 0.43/1.13 inference(demodulation,[status(thm)],[c_1729,c_2606])).
% 0.43/1.13
% 0.43/1.13 cnf(c_2613,plain,
% 0.43/1.13 ($less_int(sP1_iProver_def,$sum_int(2,$product_int(sP2_iProver_def,2)))),
% 0.43/1.13 inference(theory_normalisation,
% 0.43/1.13 [status(thm)],
% 0.43/1.13 [c_2612,c_65,c_66,c_54,c_55])).
% 0.43/1.13
% 0.43/1.13 cnf(c_5460,plain,
% 0.43/1.13 ($false),
% 0.43/1.13 inference(smt_impl_just,
% 0.43/1.13 [status(thm)],
% 0.43/1.13 [c_2613,c_2340,c_2281,c_1791,c_1688,c_988,c_985,c_983,c_598,
% 0.43/1.13 c_989])).
% 0.43/1.13
% 0.43/1.13
% 0.43/1.13 % SZS output end CNFRefutation for theBenchmark.p
% 0.43/1.13
% 0.43/1.13
%------------------------------------------------------------------------------