%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWW616_2 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 : Tue Sep 29 01:40:32 PM UTC 2026
% Result : Theorem 0.73s 0.41s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW616_2 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 % Computer : n013.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Mon Sep 28 14:22:09 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.24/0.28 Running first-order model finding
% 0.24/0.28 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.73/0.41 % (1213507)Will run a generic schedule for satisfiability detection.
% 0.73/0.41 % (1213514)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1558165802:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.73/0.41 % (1213512)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1112210917_2999 on theBenchmark for (2999ds/0Mi)
% 0.73/0.41 % (1213512)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.73/0.41 % (1213512)Terminated due to inappropriate strategy.
% 0.73/0.41 % (1213512)------------------------------
% 0.73/0.41 % (1213512)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.41 % (1213512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.41 % (1213512)CaDiCaL version: 2.1.3
% 0.73/0.41 % (1213512)Termination reason: Inappropriate
% 0.73/0.41 % (1213512)Time elapsed: 0.004 s
% 0.73/0.41 % (1213512)Peak memory usage: 11 MB
% 0.73/0.41 % (1213512)Instructions burned: 5 (million)
% 0.73/0.41 % (1213512)------------------------------
% 0.73/0.41 % (1213512)------------------------------
% 0.73/0.41 % (1213513)% WARNING: option uhcvi not known.
% 0.73/0.41 % (1213516)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3421814785:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.73/0.41 % (1213515)dis+10_1_sil=32000:sp=arity:random_seed=3373789850:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.73/0.41 % (1213517)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=427783302:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.73/0.41 % (1213518)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3919166148:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.73/0.41 % (1213513)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2707725971:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.73/0.41 % (1213521)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1076256289:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.73/0.41 % (1213521)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.73/0.41 % (1213521)Terminated due to inappropriate strategy.
% 0.73/0.41 % (1213521)------------------------------
% 0.73/0.41 % (1213521)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.41 % (1213521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.41 % (1213521)CaDiCaL version: 2.1.3
% 0.73/0.41 % (1213521)Termination reason: Inappropriate
% 0.73/0.41 % (1213521)Time elapsed: 0.007 s
% 0.73/0.41 % (1213521)Peak memory usage: 11 MB
% 0.73/0.41 % (1213521)Instructions burned: 5 (million)
% 0.73/0.41 % (1213521)------------------------------
% 0.73/0.41 % (1213521)------------------------------
% 0.73/0.41 % (1213528)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2411863723:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.73/0.41 % (1213514) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1213507-1213514"...
% 0.73/0.41 % (1213514)...printing done.
% 0.73/0.41 % (1213514)Refutation found. Thanks to Tanya!
% 0.73/0.41 % SZS status Theorem for theBenchmark
% 0.73/0.41 % SZS output start Proof for theBenchmark
% 0.73/0.41 tff(type_def_5, type, uni: $tType).
% 0.73/0.41 tff(type_def_6, type, ty: $tType).
% 0.73/0.41 tff(type_def_7, type, bool: $tType).
% 0.73/0.41 tff(type_def_8, type, tuple0: $tType).
% 0.73/0.41 tff(type_def_9, type, map_int_int: $tType).
% 0.73/0.41 tff(type_def_10, type, array_int: $tType).
% 0.73/0.41 tff(func_def_0, type, witness: ty > uni).
% 0.73/0.41 tff(func_def_1, type, int: ty).
% 0.73/0.41 tff(func_def_2, type, real: ty).
% 0.73/0.41 tff(func_def_3, type, bool1: ty).
% 0.73/0.41 tff(func_def_4, type, true: bool).
% 0.73/0.41 tff(func_def_5, type, false: bool).
% 0.73/0.41 tff(func_def_6, type, match_bool: (ty * bool * uni * uni) > uni).
% 0.73/0.41 tff(func_def_7, type, tuple01: ty).
% 0.73/0.41 tff(func_def_8, type, tuple02: tuple0).
% 0.73/0.41 tff(func_def_9, type, qtmark: ty).
% 0.73/0.41 tff(func_def_12, type, ref: ty > ty).
% 0.73/0.41 tff(func_def_13, type, mk_ref: (ty * uni) > uni).
% 0.73/0.41 tff(func_def_14, type, contents: (ty * uni) > uni).
% 0.73/0.41 tff(func_def_15, type, abs: $int > $int).
% 0.73/0.41 tff(func_def_17, type, div: ($int * $int) > $int).
% 0.73/0.41 tff(func_def_18, type, mod: ($int * $int) > $int).
% 0.73/0.41 tff(func_def_21, type, map: (ty * ty) > ty).
% 0.73/0.41 tff(func_def_22, type, get: (ty * ty * uni * uni) > uni).
% 0.73/0.41 tff(func_def_23, type, set: (ty * ty * uni * uni * uni) > uni).
% 0.73/0.41 tff(func_def_24, type, const: (ty * ty * uni) > uni).
% 0.73/0.41 tff(func_def_25, type, array: ty > ty).
% 0.73/0.41 tff(func_def_26, type, mk_array: (ty * $int * uni) > uni).
% 0.73/0.41 tff(func_def_27, type, length: (ty * uni) > $int).
% 0.73/0.41 tff(func_def_28, type, elts: (ty * uni) > uni).
% 0.73/0.41 tff(func_def_29, type, get1: (ty * uni * $int) > uni).
% 0.73/0.41 tff(func_def_30, type, t2tb: $int > uni).
% 0.73/0.41 tff(func_def_31, type, tb2t: uni > $int).
% 0.73/0.41 tff(func_def_32, type, set1: (ty * uni * $int * uni) > uni).
% 0.73/0.41 tff(func_def_33, type, make: (ty * $int * uni) > uni).
% 0.73/0.41 tff(func_def_34, type, sum: (map_int_int * $int * $int) > $int).
% 0.73/0.41 tff(func_def_35, type, t2tb1: map_int_int > uni).
% 0.73/0.41 tff(func_def_36, type, tb2t1: uni > map_int_int).
% 0.73/0.41 tff(func_def_38, type, sum1: (array_int * $int * $int) > $int).
% 0.73/0.41 tff(func_def_39, type, t2tb2: array_int > uni).
% 0.73/0.41 tff(func_def_40, type, tb2t2: uni > array_int).
% 0.73/0.41 tff(func_def_42, type, sK0: (map_int_int * map_int_int * $int * $int) > $int).
% 0.73/0.41 tff(func_def_43, type, sK1: $int).
% 0.73/0.41 tff(func_def_44, type, sK2: map_int_int).
% 0.73/0.41 tff(func_def_45, type, sK3: $int).
% 0.73/0.41 tff(func_def_46, type, sK4: $int).
% 0.73/0.41 tff(func_def_47, type, sK5: $int).
% 0.73/0.41 tff(func_def_48, type, sK6: $int).
% 0.73/0.41 tff(func_def_49, type, sK7: $int).
% 0.73/0.41 tff(func_def_50, type, sK8: $int).
% 0.73/0.41 tff(func_def_51, type, sK9: $int).
% 0.73/0.41 tff(func_def_52, type, sK10: $int).
% 0.73/0.41 tff(func_def_53, type, sK11: $int).
% 0.73/0.41 tff(func_def_54, type, sK12: $int).
% 0.73/0.41 tff(pred_def_1, type, sort: (ty * uni) > $o).
% 0.73/0.41 tff(pred_def_4, type, maxsublo: (array_int * $int * $int) > $o).
% 0.73/0.41 tff(pred_def_5, type, maxsub: (array_int * $int) > $o).
% 0.73/0.41 tff(f64,conjecture,(
% 0.73/0.41 ! [X0 : $int,X1 : map_int_int,X2 : $int,X3 : $int] : (($lesseq(0,X0) & $lesseq(0,X2) & $lesseq(X2,X3) & $lesseq(X3,X0)) => (X3 != X2 => ! [X4 : $int] : (X4 = $sum(X2,div($difference(X3,X2),2)) => ! [X5 : $int] : (X5 = $sum(X2,div($difference(X3,X2),2)) => ($lesseq(X2,$difference($sum(X2,div($difference(X3,X2),2)),1)) => ! [X6 : $int,X7 : $int,X8 : $int] : (($lesseq(X2,X8) & $lesseq(X8,$sum(X2,div($difference(X3,X2),2))) & $sum(X2,div($difference(X3,X2),2)) = X5 & X7 = sum(X1,X8,X5) & ! [X9 : $int] : (($less($difference(X2,1),X9) & $lesseq(X9,$sum(X2,div($difference(X3,X2),2)))) => $lesseq(sum(X1,X9,$sum(X2,div($difference(X3,X2),2))),X7)) & X6 = sum(X1,$sum($difference(X2,1),1),$sum(X2,div($difference(X3,X2),2)))) => (! [X9 : $int] : (($lesseq(X2,X9) & $lesseq(X9,$sum(X2,div($difference(X3,X2),2)))) => $lesseq(sum(X1,X9,$sum(X2,div($difference(X3,X2),2))),sum(X1,X8,$sum(X2,div($difference(X3,X2),2))))) => ! [X10 : $int] : (X10 = X7 => ($lesseq($sum(X2,div($difference(X3,X2),2)),$difference(X3,1)) => ! [X9 : $int,X11 : $int] : (($lesseq(X2,X9) & $lesseq(X9,$sum(X2,div($difference(X3,X2),2))) & $lesseq($sum(X2,div($difference(X3,X2),2)),X11) & $lesseq(X11,$sum(X2,div($difference(X3,X2),2)))) => $lesseq(sum(X1,X9,X11),X7)))))))))))),
% 0.73/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wP_parameter_maximum_subarray_rec)).
% 0.73/0.41 tff(f65,negated_conjecture,(
% 0.73/0.41 ~ ! [X0 : $int,X1 : map_int_int,X2 : $int,X3 : $int] : (($lesseq(0,X0) & $lesseq(0,X2) & $lesseq(X2,X3) & $lesseq(X3,X0)) => (X3 != X2 => ! [X4 : $int] : (X4 = $sum(X2,div($difference(X3,X2),2)) => ! [X5 : $int] : (X5 = $sum(X2,div($difference(X3,X2),2)) => ($lesseq(X2,$difference($sum(X2,div($difference(X3,X2),2)),1)) => ! [X6 : $int,X7 : $int,X8 : $int] : (($lesseq(X2,X8) & $lesseq(X8,$sum(X2,div($difference(X3,X2),2))) & $sum(X2,div($difference(X3,X2),2)) = X5 & X7 = sum(X1,X8,X5) & ! [X9 : $int] : (($less($difference(X2,1),X9) & $lesseq(X9,$sum(X2,div($difference(X3,X2),2)))) => $lesseq(sum(X1,X9,$sum(X2,div($difference(X3,X2),2))),X7)) & X6 = sum(X1,$sum($difference(X2,1),1),$sum(X2,div($difference(X3,X2),2)))) => (! [X9 : $int] : (($lesseq(X2,X9) & $lesseq(X9,$sum(X2,div($difference(X3,X2),2)))) => $lesseq(sum(X1,X9,$sum(X2,div($difference(X3,X2),2))),sum(X1,X8,$sum(X2,div($difference(X3,X2),2))))) => ! [X10 : $int] : (X10 = X7 => ($lesseq($sum(X2,div($difference(X3,X2),2)),$difference(X3,1)) => ! [X9 : $int,X11 : $int] : (($lesseq(X2,X9) & $lesseq(X9,$sum(X2,div($difference(X3,X2),2))) & $lesseq($sum(X2,div($difference(X3,X2),2)),X11) & $lesseq(X11,$sum(X2,div($difference(X3,X2),2)))) => $lesseq(sum(X1,X9,X11),X7)))))))))))),
% 0.73/0.41 inference(negated_conjecture,[status(cth)],[f64])).
% 0.73/0.41 tff(f86,plain,(
% 0.73/0.41 ~ ! [X0 : $int,X1 : map_int_int,X2 : $int,X3 : $int] : ((~$less(X0,0) & ~$less(X2,0) & ~$less(X3,X2) & ~$less(X0,X3)) => (X3 != X2 => ! [X4 : $int] : ($sum(X2,div($sum(X3,$uminus(X2)),2)) = X4 => ! [X5 : $int] : ($sum(X2,div($sum(X3,$uminus(X2)),2)) = X5 => (~$less($sum($sum(X2,div($sum(X3,$uminus(X2)),2)),$uminus(1)),X2) => ! [X6 : $int,X7 : $int,X8 : $int] : ((~$less(X8,X2) & ~$less($sum(X2,div($sum(X3,$uminus(X2)),2)),X8) & $sum(X2,div($sum(X3,$uminus(X2)),2)) = X5 & X7 = sum(X1,X8,X5) & ! [X9 : $int] : (($less($sum(X2,$uminus(1)),X9) & ~$less($sum(X2,div($sum(X3,$uminus(X2)),2)),X9)) => ~$less(X7,sum(X1,X9,$sum(X2,div($sum(X3,$uminus(X2)),2))))) & sum(X1,$sum($sum(X2,$uminus(1)),1),$sum(X2,div($sum(X3,$uminus(X2)),2))) = X6) => (! [X9 : $int] : ((~$less(X9,X2) & ~$less($sum(X2,div($sum(X3,$uminus(X2)),2)),X9)) => ~$less(sum(X1,X8,$sum(X2,div($sum(X3,$uminus(X2)),2))),sum(X1,X9,$sum(X2,div($sum(X3,$uminus(X2)),2))))) => ! [X10 : $int] : (X10 = X7 => (~$less($sum(X3,$uminus(1)),$sum(X2,div($sum(X3,$uminus(X2)),2))) => ! [X9 : $int,X11 : $int] : ((~$less(X9,X2) & ~$less($sum(X2,div($sum(X3,$uminus(X2)),2)),X9) & ~$less(X11,$sum(X2,div($sum(X3,$uminus(X2)),2))) & ~$less($sum(X2,div($sum(X3,$uminus(X2)),2)),X11)) => ~$less(X7,sum(X1,X9,X11))))))))))))),
% 0.73/0.41 inference(theory_normalization,[],[f65])).
% 0.73/0.41 tff(f94,definition,(
% 0.73/0.41 ( ! [X0 : $int,X1 : $int] : ($less(X1,X0) | $less(X0,X1) | X0 = X1) )),
% 0.73/0.41 introduced(theory,[tha_order_totality])).
% 0.73/0.41 tff(f105,plain,(
% 0.73/0.41 ~ ! [X0 : $int,X1 : map_int_int,X2 : $int,X3 : $int] : ((~$less(X0,0) & ~$less(X2,0) & ~$less(X3,X2) & ~$less(X0,X3)) => (X3 != X2 => ! [X4 : $int] : ($sum(X2,div($sum(X3,$uminus(X2)),2)) = X4 => ! [X5 : $int] : ($sum(X2,div($sum(X3,$uminus(X2)),2)) = X5 => (~$less($sum($sum(X2,div($sum(X3,$uminus(X2)),2)),$uminus(1)),X2) => ! [X6 : $int,X7 : $int,X8 : $int] : ((~$less(X8,X2) & ~$less($sum(X2,div($sum(X3,$uminus(X2)),2)),X8) & $sum(X2,div($sum(X3,$uminus(X2)),2)) = X5 & X7 = sum(X1,X8,X5) & ! [X9 : $int] : (($less($sum(X2,$uminus(1)),X9) & ~$less($sum(X2,div($sum(X3,$uminus(X2)),2)),X9)) => ~$less(X7,sum(X1,X9,$sum(X2,div($sum(X3,$uminus(X2)),2))))) & sum(X1,$sum($sum(X2,$uminus(1)),1),$sum(X2,div($sum(X3,$uminus(X2)),2))) = X6) => (! [X10 : $int] : ((~$less(X10,X2) & ~$less($sum(X2,div($sum(X3,$uminus(X2)),2)),X10)) => ~$less(sum(X1,X8,$sum(X2,div($sum(X3,$uminus(X2)),2))),sum(X1,X10,$sum(X2,div($sum(X3,$uminus(X2)),2))))) => ! [X11 : $int] : (X7 = X11 => (~$less($sum(X3,$uminus(1)),$sum(X2,div($sum(X3,$uminus(X2)),2))) => ! [X12 : $int,X13 : $int] : ((~$less(X12,X2) & ~$less($sum(X2,div($sum(X3,$uminus(X2)),2)),X12) & ~$less(X13,$sum(X2,div($sum(X3,$uminus(X2)),2))) & ~$less($sum(X2,div($sum(X3,$uminus(X2)),2)),X13)) => ~$less(X7,sum(X1,X12,X13))))))))))))),
% 0.73/0.41 inference(rectify,[],[f86])).
% 0.73/0.41 tff(f147,plain,(
% 0.73/0.41 ? [X0 : $int,X1 : map_int_int,X2 : $int,X3 : $int] : ((? [X4 : $int] : (? [X5 : $int] : ((? [X6 : $int,X7 : $int,X8 : $int] : ((? [X11 : $int] : ((? [X12 : $int,X13 : $int] : ($less(X7,sum(X1,X12,X13)) & (~$less(X12,X2) & ~$less($sum(X2,div($sum(X3,$uminus(X2)),2)),X12) & ~$less(X13,$sum(X2,div($sum(X3,$uminus(X2)),2))) & ~$less($sum(X2,div($sum(X3,$uminus(X2)),2)),X13))) & ~$less($sum(X3,$uminus(1)),$sum(X2,div($sum(X3,$uminus(X2)),2)))) & X7 = X11) & ! [X10 : $int] : (~$less(sum(X1,X8,$sum(X2,div($sum(X3,$uminus(X2)),2))),sum(X1,X10,$sum(X2,div($sum(X3,$uminus(X2)),2)))) | ($less(X10,X2) | $less($sum(X2,div($sum(X3,$uminus(X2)),2)),X10)))) & (~$less(X8,X2) & ~$less($sum(X2,div($sum(X3,$uminus(X2)),2)),X8) & $sum(X2,div($sum(X3,$uminus(X2)),2)) = X5 & X7 = sum(X1,X8,X5) & ! [X9 : $int] : (~$less(X7,sum(X1,X9,$sum(X2,div($sum(X3,$uminus(X2)),2)))) | (~$less($sum(X2,$uminus(1)),X9) | $less($sum(X2,div($sum(X3,$uminus(X2)),2)),X9))) & sum(X1,$sum($sum(X2,$uminus(1)),1),$sum(X2,div($sum(X3,$uminus(X2)),2))) = X6)) & ~$less($sum($sum(X2,div($sum(X3,$uminus(X2)),2)),$uminus(1)),X2)) & $sum(X2,div($sum(X3,$uminus(X2)),2)) = X5) & $sum(X2,div($sum(X3,$uminus(X2)),2)) = X4) & X3 != X2) & (~$less(X0,0) & ~$less(X2,0) & ~$less(X3,X2) & ~$less(X0,X3)))),
% 0.73/0.41 inference(ennf_transformation,[],[f105])).
% 0.73/0.41 tff(f148,plain,(
% 0.73/0.41 ? [X0 : $int,X1 : map_int_int,X2 : $int,X3 : $int] : (? [X4 : $int] : (? [X5 : $int] : (? [X6 : $int,X7 : $int,X8 : $int] : (? [X11 : $int] : (? [X12 : $int,X13 : $int] : ($less(X7,sum(X1,X12,X13)) & ~$less(X12,X2) & ~$less($sum(X2,div($sum(X3,$uminus(X2)),2)),X12) & ~$less(X13,$sum(X2,div($sum(X3,$uminus(X2)),2))) & ~$less($sum(X2,div($sum(X3,$uminus(X2)),2)),X13)) & ~$less($sum(X3,$uminus(1)),$sum(X2,div($sum(X3,$uminus(X2)),2))) & X7 = X11) & ! [X10 : $int] : (~$less(sum(X1,X8,$sum(X2,div($sum(X3,$uminus(X2)),2))),sum(X1,X10,$sum(X2,div($sum(X3,$uminus(X2)),2)))) | $less(X10,X2) | $less($sum(X2,div($sum(X3,$uminus(X2)),2)),X10)) & ~$less(X8,X2) & ~$less($sum(X2,div($sum(X3,$uminus(X2)),2)),X8) & $sum(X2,div($sum(X3,$uminus(X2)),2)) = X5 & X7 = sum(X1,X8,X5) & ! [X9 : $int] : (~$less(X7,sum(X1,X9,$sum(X2,div($sum(X3,$uminus(X2)),2)))) | ~$less($sum(X2,$uminus(1)),X9) | $less($sum(X2,div($sum(X3,$uminus(X2)),2)),X9)) & sum(X1,$sum($sum(X2,$uminus(1)),1),$sum(X2,div($sum(X3,$uminus(X2)),2))) = X6) & ~$less($sum($sum(X2,div($sum(X3,$uminus(X2)),2)),$uminus(1)),X2) & $sum(X2,div($sum(X3,$uminus(X2)),2)) = X5) & $sum(X2,div($sum(X3,$uminus(X2)),2)) = X4) & X3 != X2 & ~$less(X0,0) & ~$less(X2,0) & ~$less(X3,X2) & ~$less(X0,X3))),
% 0.73/0.41 inference(flattening,[],[f147])).
% 0.73/0.41 tff(f152,plain,(
% 0.73/0.41 ? [X0 : $int,X1 : map_int_int,X2 : $int,X3 : $int] : (? [X4 : $int] : (? [X5 : $int] : (? [X6 : $int,X7 : $int,X8 : $int] : (? [X9 : $int] : (? [X10 : $int,X11 : $int] : ($less(X7,sum(X1,X10,X11)) & ~$less(X10,X2) & ~$less($sum(X2,div($sum(X3,$uminus(X2)),2)),X10) & ~$less(X11,$sum(X2,div($sum(X3,$uminus(X2)),2))) & ~$less($sum(X2,div($sum(X3,$uminus(X2)),2)),X11)) & ~$less($sum(X3,$uminus(1)),$sum(X2,div($sum(X3,$uminus(X2)),2))) & X7 = X9) & ! [X12 : $int] : (~$less(sum(X1,X8,$sum(X2,div($sum(X3,$uminus(X2)),2))),sum(X1,X12,$sum(X2,div($sum(X3,$uminus(X2)),2)))) | $less(X12,X2) | $less($sum(X2,div($sum(X3,$uminus(X2)),2)),X12)) & ~$less(X8,X2) & ~$less($sum(X2,div($sum(X3,$uminus(X2)),2)),X8) & $sum(X2,div($sum(X3,$uminus(X2)),2)) = X5 & X7 = sum(X1,X8,X5) & ! [X13 : $int] : (~$less(X7,sum(X1,X13,$sum(X2,div($sum(X3,$uminus(X2)),2)))) | ~$less($sum(X2,$uminus(1)),X13) | $less($sum(X2,div($sum(X3,$uminus(X2)),2)),X13)) & sum(X1,$sum($sum(X2,$uminus(1)),1),$sum(X2,div($sum(X3,$uminus(X2)),2))) = X6) & ~$less($sum($sum(X2,div($sum(X3,$uminus(X2)),2)),$uminus(1)),X2) & $sum(X2,div($sum(X3,$uminus(X2)),2)) = X5) & $sum(X2,div($sum(X3,$uminus(X2)),2)) = X4) & X3 != X2 & ~$less(X0,0) & ~$less(X2,0) & ~$less(X3,X2) & ~$less(X0,X3))),
% 0.73/0.41 inference(rectify,[],[f148])).
% 0.73/0.41 tff(f153,plain,(
% 0.73/0.41 ((((($less(sK8,sum(sK2,sK11,sK12)) & ~$less(sK11,sK3) & ~$less($sum(sK3,div($sum(sK4,$uminus(sK3)),2)),sK11) & ~$less(sK12,$sum(sK3,div($sum(sK4,$uminus(sK3)),2))) & ~$less($sum(sK3,div($sum(sK4,$uminus(sK3)),2)),sK12)) & ~$less($sum(sK4,$uminus(1)),$sum(sK3,div($sum(sK4,$uminus(sK3)),2))) & sK8 = sK10) & ! [X12 : $int] : (~$less(sum(sK2,sK9,$sum(sK3,div($sum(sK4,$uminus(sK3)),2))),sum(sK2,X12,$sum(sK3,div($sum(sK4,$uminus(sK3)),2)))) | $less(X12,sK3) | $less($sum(sK3,div($sum(sK4,$uminus(sK3)),2)),X12)) & ~$less(sK9,sK3) & ~$less($sum(sK3,div($sum(sK4,$uminus(sK3)),2)),sK9) & sK6 = $sum(sK3,div($sum(sK4,$uminus(sK3)),2)) & sK8 = sum(sK2,sK9,sK6) & ! [X13 : $int] : (~$less(sK8,sum(sK2,X13,$sum(sK3,div($sum(sK4,$uminus(sK3)),2)))) | ~$less($sum(sK3,$uminus(1)),X13) | $less($sum(sK3,div($sum(sK4,$uminus(sK3)),2)),X13)) & sK7 = sum(sK2,$sum($sum(sK3,$uminus(1)),1),$sum(sK3,div($sum(sK4,$uminus(sK3)),2)))) & ~$less($sum($sum(sK3,div($sum(sK4,$uminus(sK3)),2)),$uminus(1)),sK3) & sK6 = $sum(sK3,div($sum(sK4,$uminus(sK3)),2))) & sK5 = $sum(sK3,div($sum(sK4,$uminus(sK3)),2))) & sK3 != sK4 & ~$less(sK1,0) & ~$less(sK3,0) & ~$less(sK4,sK3) & ~$less(sK1,sK4)),
% 0.73/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4),skolemize(X4,sK5),skolemize(X5,sK6),skolemize(X6,sK7),skolemize(X7,sK8),skolemize(X8,sK9),skolemize(X9,sK10),skolemize(X10,sK11),skolemize(X11,sK12)],[f152])).
% 0.73/0.41 tff(f227,plain,(
% 0.73/0.41 sK5 = $sum(sK3,div($sum(sK4,$uminus(sK3)),2))),
% 0.73/0.41 inference(cnf_transformation,[],[f153])).
% 0.73/0.41 tff(f228,plain,(
% 0.73/0.41 sK6 = $sum(sK3,div($sum(sK4,$uminus(sK3)),2))),
% 0.73/0.41 inference(cnf_transformation,[],[f153])).
% 0.73/0.41 tff(f232,plain,(
% 0.73/0.41 sK8 = sum(sK2,sK9,sK6)),
% 0.73/0.41 inference(cnf_transformation,[],[f153])).
% 0.73/0.41 tff(f236,plain,(
% 0.73/0.41 ( ! [X12 : $int] : (~$less(sum(sK2,sK9,$sum(sK3,div($sum(sK4,$uminus(sK3)),2))),sum(sK2,X12,$sum(sK3,div($sum(sK4,$uminus(sK3)),2)))) | $less(X12,sK3) | $less($sum(sK3,div($sum(sK4,$uminus(sK3)),2)),X12)) )),
% 0.73/0.41 inference(cnf_transformation,[],[f153])).
% 0.73/0.41 tff(f237,plain,(
% 0.73/0.41 sK8 = sK10),
% 0.73/0.41 inference(cnf_transformation,[],[f153])).
% 0.73/0.41 tff(f239,plain,(
% 0.73/0.41 ~$less($sum(sK3,div($sum(sK4,$uminus(sK3)),2)),sK12)),
% 0.73/0.41 inference(cnf_transformation,[],[f153])).
% 0.73/0.41 tff(f240,plain,(
% 0.73/0.41 ~$less(sK12,$sum(sK3,div($sum(sK4,$uminus(sK3)),2)))),
% 0.73/0.41 inference(cnf_transformation,[],[f153])).
% 0.73/0.41 tff(f241,plain,(
% 0.73/0.41 ~$less($sum(sK3,div($sum(sK4,$uminus(sK3)),2)),sK11)),
% 0.73/0.41 inference(cnf_transformation,[],[f153])).
% 0.73/0.41 tff(f242,plain,(
% 0.73/0.41 ~$less(sK11,sK3)),
% 0.73/0.41 inference(cnf_transformation,[],[f153])).
% 0.73/0.41 tff(f243,plain,(
% 0.73/0.41 $less(sK8,sum(sK2,sK11,sK12))),
% 0.73/0.41 inference(cnf_transformation,[],[f153])).
% 0.73/0.41 tff(f247,plain,(
% 0.73/0.41 $less(sK10,sum(sK2,sK11,sK12))),
% 0.73/0.41 inference(definition_unfolding,[],[f243,f237])).
% 0.73/0.41 tff(f248,plain,(
% 0.73/0.41 sK10 = sum(sK2,sK9,sK6)),
% 0.73/0.41 inference(definition_unfolding,[],[f232,f237])).
% 0.73/0.41 tff(f271,plain,(
% 0.73/0.41 sK5 = sK6),
% 0.73/0.41 inference(superposition,[],[f228,f227])).
% 0.73/0.41 tff(f276,plain,(
% 0.73/0.41 ~$less(sK6,sK11)),
% 0.73/0.41 inference(superposition,[],[f241,f228])).
% 0.73/0.41 tff(f318,plain,(
% 0.73/0.41 ( ! [X12 : $int] : (~$less(sum(sK2,sK9,sK5),sum(sK2,X12,sK5)) | $less(X12,sK3) | $less($sum(sK3,div($sum(sK4,$uminus(sK3)),2)),X12)) )),
% 0.73/0.41 inference(forward_demodulation,[],[f236,f227])).
% 0.73/0.41 tff(f319,plain,(
% 0.73/0.41 ( ! [X12 : $int] : (~$less(sum(sK2,sK9,sK6),sum(sK2,X12,sK6)) | $less(X12,sK3) | $less($sum(sK3,div($sum(sK4,$uminus(sK3)),2)),X12)) )),
% 0.73/0.41 inference(forward_demodulation,[],[f318,f271])).
% 0.73/0.41 tff(f320,plain,(
% 0.73/0.41 ( ! [X12 : $int] : (~$less(sK10,sum(sK2,X12,sK6)) | $less(X12,sK3) | $less($sum(sK3,div($sum(sK4,$uminus(sK3)),2)),X12)) )),
% 0.73/0.41 inference(forward_demodulation,[],[f319,f248])).
% 0.73/0.41 tff(f1565,plain,(
% 0.73/0.41 $less(sK12,$sum(sK3,div($sum(sK4,$uminus(sK3)),2))) | sK12 = $sum(sK3,div($sum(sK4,$uminus(sK3)),2))),
% 0.73/0.41 inference(resolution,[],[f94,f239])).
% 0.73/0.41 tff(f1597,plain,(
% 0.73/0.41 sK12 = $sum(sK3,div($sum(sK4,$uminus(sK3)),2))),
% 0.73/0.41 inference(forward_subsumption_resolution,[],[f1565,f240])).
% 0.73/0.41 tff(f1622,plain,(
% 0.73/0.41 sK6 = sK12),
% 0.73/0.41 inference(forward_demodulation,[],[f1597,f228])).
% 0.73/0.41 tff(f1663,plain,(
% 0.73/0.41 $less(sK10,sum(sK2,sK11,sK6))),
% 0.73/0.41 inference(superposition,[],[f247,f1622])).
% 0.73/0.41 tff(f1677,plain,(
% 0.73/0.41 ( ! [X12 : $int] : ($less(sK5,X12) | ~$less(sK10,sum(sK2,X12,sK6)) | $less(X12,sK3)) )),
% 0.73/0.41 inference(forward_demodulation,[],[f320,f227])).
% 0.73/0.41 tff(f1680,plain,(
% 0.73/0.41 ( ! [X12 : $int] : (~$less(sK10,sum(sK2,X12,sK6)) | $less(sK6,X12) | $less(X12,sK3)) )),
% 0.73/0.41 inference(forward_demodulation,[],[f1677,f271])).
% 0.73/0.41 tff(f5576,plain,(
% 0.73/0.41 $less(sK6,sK11) | $less(sK11,sK3)),
% 0.73/0.41 inference(resolution,[],[f1680,f1663])).
% 0.73/0.41 tff(f5582,plain,(
% 0.73/0.41 $less(sK11,sK3)),
% 0.73/0.41 inference(forward_subsumption_resolution,[],[f5576,f276])).
% 0.73/0.41 tff(f5584,plain,(
% 0.73/0.41 $false),
% 0.73/0.41 inference(forward_subsumption_resolution,[],[f5582,f242])).
% 0.73/0.41 % SZS output end Proof for theBenchmark
% 0.73/0.41 % (1213514)------------------------------
% 0.73/0.41 % (1213514)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.41 % (1213514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.41 % (1213514)CaDiCaL version: 2.1.3
% 0.73/0.41 % (1213514)Termination reason: Refutation
% 0.73/0.41 % (1213514)Time elapsed: 0.097 s
% 0.73/0.41 % (1213514)Peak memory usage: 14 MB
% 0.73/0.41 % (1213514)Instructions burned: 167 (million)
% 0.73/0.41 % (1213507)Success in time 0.123 s
% 0.73/0.41 % Vampire exiting
%------------------------------------------------------------------------------