%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV514^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 : Wed Sep 30 08:38:47 AM UTC 2026
% Result : Theorem 0.23s 0.31s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV514^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n009.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 15:55:15 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.31 % (4176075)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.31 % (4176085)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4217209313:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.31 % (4176086)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.31 % (4176086)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.23/0.31 % (4176081)lrs+10_16_si=on:nwc=1.5:random_seed=1155594871:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.31 % (4176080)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3124906394:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.31 % (4176082)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3936862927:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.31 % (4176084)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=307155253:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.31 % (4176083)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=111206065:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.23/0.31 % (4176086)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1099099425:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.31 % (4176082)Instruction limit reached!
% 0.23/0.31 % (4176082)------------------------------
% 0.23/0.31 % (4176082)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (4176082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (4176082)CaDiCaL version: 2.1.3
% 0.23/0.31 % (4176082)Termination reason: Instruction limit
% 0.23/0.31 % (4176082)Termination phase: Saturation
% 0.23/0.31 % (4176082)Time elapsed: 0.003 s
% 0.23/0.31 % (4176082)Peak memory usage: 12 MB
% 0.23/0.31 % (4176082)Instructions burned: 3 (million)
% 0.23/0.31 % (4176083) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4176075-4176083"...
% 0.23/0.31 % (4176084) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4176075-4176084"...
% 0.23/0.31 % (4176080) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4176075-4176080"...
% 0.23/0.31 % (4176084)...printing done.
% 0.23/0.31 % (4176083)...printing done.
% 0.23/0.31 % (4176080)...printing done.
% 0.23/0.31 % (4176084)Refutation found. Thanks to Tanya!
% 0.23/0.31 % SZS status Theorem for theBenchmark
% 0.23/0.31 % SZS output start Proof for theBenchmark
% 0.23/0.31 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.23/0.31 thf(type_def_6, type, 'type/nums/num': $tType).
% 0.23/0.31 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.31 thf(func_def_0, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.23/0.31 thf(func_def_1, type, 'const/realax/real_of_num': ('type/nums/num' > 'type/realax/real')).
% 0.23/0.31 thf(func_def_2, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.23/0.31 thf(func_def_3, type, 'const/nums/NUMERAL': ('type/nums/num' > 'type/nums/num')).
% 0.23/0.31 thf(func_def_4, type, 'const/nums/_0': 'type/nums/num').
% 0.23/0.31 thf(func_def_5, type, 'const/iterate/sum': !>[X0: $tType]:(((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real'))).
% 0.23/0.31 thf(func_def_6, type, 'const/iterate/..': ('type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o)).
% 0.23/0.31 thf(func_def_7, type, 'const/arith/<=': ('type/nums/num' > 'type/nums/num' > $o)).
% 0.23/0.31 thf(func_def_11, type, sK0: !>[X0: $tType]:(((X0 > 'type/realax/real') > (X0 > $o) > X0))).
% 0.23/0.31 thf(func_def_12, type, sK1: 'type/nums/num').
% 0.23/0.31 thf(func_def_13, type, sK2: ('type/nums/num' > 'type/realax/real')).
% 0.23/0.31 thf(func_def_14, type, sK3: 'type/nums/num').
% 0.23/0.31 thf(f1,axiom,(
% 0.23/0.31 ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > 'type/realax/real')] : (! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X2) => ('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (X1 @ X3))) => ('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ X0 @ X2 @ X1)))),
% 0.23/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_POS_LE_')).
% 0.23/0.31 thf(f2,axiom,(
% 0.23/0.31 ! [X0 : 'type/nums/num',X2 : 'type/nums/num',X1 : 'type/nums/num'] : (('const/arith/<=' @ X0 @ X2) & ('const/arith/<=' @ X2 @ X1) = (('const/sets/IN' @ 'type/nums/num' @ X2 @ ('const/iterate/..' @ X0 @ X1))))),
% 0.23/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/IN_NUMSEG_')).
% 0.23/0.31 thf(f3,conjecture,(
% 0.23/0.31 ! [X0 : 'type/nums/num',X2 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num'] : (! [X3 : 'type/nums/num'] : ((('const/arith/<=' @ X3 @ X1) & ('const/arith/<=' @ X0 @ X3)) => ('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (X2 @ X3))) => ('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2)))),
% 0.23/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_POS_LE_NUMSEG_')).
% 0.23/0.31 thf(f4,negated_conjecture,(
% 0.23/0.31 ~ ! [X0 : 'type/nums/num',X2 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num'] : (! [X3 : 'type/nums/num'] : ((('const/arith/<=' @ X3 @ X1) & ('const/arith/<=' @ X0 @ X3)) => ('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (X2 @ X3))) => ('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2)))),
% 0.23/0.31 inference(negated_conjecture,[status(cth)],[f3])).
% 0.23/0.31 thf(f5,plain,(
% 0.23/0.31 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : (('const/arith/<=' @ X0 @ X1) & ('const/arith/<=' @ X1 @ X2) = (('const/sets/IN' @ 'type/nums/num' @ X1 @ ('const/iterate/..' @ X0 @ X2))))),
% 0.23/0.31 inference(rectify,[],[f2])).
% 0.23/0.31 thf(f6,plain,(
% 0.23/0.31 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : (($true = (('const/sets/IN' @ 'type/nums/num' @ X1 @ ('const/iterate/..' @ X0 @ X2)))) <=> (($true = (('const/arith/<=' @ X1 @ X2))) & ((('const/arith/<=' @ X0 @ X1)) = $true)))),
% 0.23/0.31 inference(fool_elimination,[],[f5])).
% 0.23/0.31 thf(f7,plain,(
% 0.23/0.31 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > 'type/realax/real')] : (! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) => ('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (X2 @ X3))) => ('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ X0 @ X1 @ X2)))),
% 0.23/0.31 inference(rectify,[],[f1])).
% 0.23/0.31 thf(f8,plain,(
% 0.23/0.31 ! [X0 : $tType,X2 : (X0 > 'type/realax/real'),X1 : (X0 > $o)] : (! [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X1)) = $true) => ($true = (('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (X2 @ X3))))) => ((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ X0 @ X1 @ X2))) = $true))),
% 0.23/0.31 inference(fool_elimination,[],[f7])).
% 0.23/0.31 thf(f9,plain,(
% 0.23/0.31 ~ ! [X0 : 'type/nums/num',X1 : ('type/nums/num' > 'type/realax/real'),X2 : 'type/nums/num'] : (! [X3 : 'type/nums/num'] : ((('const/arith/<=' @ X3 @ X2) & ('const/arith/<=' @ X0 @ X3)) => ('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (X1 @ X3))) => ('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X2) @ X1)))),
% 0.23/0.31 inference(rectify,[],[f4])).
% 0.23/0.31 thf(f10,plain,(
% 0.23/0.31 ~ ! [X2 : 'type/nums/num',X1 : ('type/nums/num' > 'type/realax/real'),X0 : 'type/nums/num'] : (! [X3 : 'type/nums/num'] : ((($true = (('const/arith/<=' @ X3 @ X2))) & ((('const/arith/<=' @ X0 @ X3)) = $true)) => ($true = (('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (X1 @ X3))))) => ((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X2) @ X1))) = $true))),
% 0.23/0.31 inference(fool_elimination,[],[f9])).
% 0.23/0.31 thf(f11,plain,(
% 0.23/0.31 ? [X2 : 'type/nums/num',X1 : ('type/nums/num' > 'type/realax/real'),X0 : 'type/nums/num'] : (((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X2) @ X1))) != $true) & ! [X3 : 'type/nums/num'] : (($true = (('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (X1 @ X3)))) | (($true != (('const/arith/<=' @ X3 @ X2))) | ((('const/arith/<=' @ X0 @ X3)) != $true))))),
% 0.23/0.31 inference(ennf_transformation,[],[f10])).
% 0.23/0.31 thf(f12,plain,(
% 0.23/0.31 ? [X0 : 'type/nums/num',X1 : ('type/nums/num' > 'type/realax/real'),X2 : 'type/nums/num'] : (! [X3 : 'type/nums/num'] : (($true != (('const/arith/<=' @ X3 @ X2))) | ((('const/arith/<=' @ X0 @ X3)) != $true) | ($true = (('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (X1 @ X3))))) & ((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X2) @ X1))) != $true))),
% 0.23/0.31 inference(flattening,[],[f11])).
% 0.23/0.31 thf(f13,plain,(
% 0.23/0.31 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > 'type/realax/real')] : (? [X3 : X0] : (($true != (('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (X2 @ X3)))) & ((('const/sets/IN' @ X0 @ X3 @ X1)) = $true)) | ((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ X0 @ X1 @ X2))) = $true))),
% 0.23/0.31 inference(ennf_transformation,[],[f8])).
% 0.23/0.31 thf(f14,plain,(
% 0.23/0.31 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : ((($true = (('const/sets/IN' @ 'type/nums/num' @ X1 @ ('const/iterate/..' @ X0 @ X2)))) | (($true != (('const/arith/<=' @ X1 @ X2))) | ((('const/arith/<=' @ X0 @ X1)) != $true))) & ((($true = (('const/arith/<=' @ X1 @ X2))) & ((('const/arith/<=' @ X0 @ X1)) = $true)) | ($true != (('const/sets/IN' @ 'type/nums/num' @ X1 @ ('const/iterate/..' @ X0 @ X2))))))),
% 0.23/0.31 inference(nnf_transformation,[],[f6])).
% 0.23/0.31 thf(f15,plain,(
% 0.23/0.31 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : ((($true = (('const/sets/IN' @ 'type/nums/num' @ X1 @ ('const/iterate/..' @ X0 @ X2)))) | ($true != (('const/arith/<=' @ X1 @ X2))) | ((('const/arith/<=' @ X0 @ X1)) != $true)) & ((($true = (('const/arith/<=' @ X1 @ X2))) & ((('const/arith/<=' @ X0 @ X1)) = $true)) | ($true != (('const/sets/IN' @ 'type/nums/num' @ X1 @ ('const/iterate/..' @ X0 @ X2))))))),
% 0.23/0.31 inference(flattening,[],[f14])).
% 0.23/0.31 thf(f16,plain,(
% 0.23/0.31 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > 'type/realax/real')] : ((($true != (('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (X2 @ (sK0 @ X0 @ X2 @ X1))))) & ($true = (('const/sets/IN' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X1)))) | ((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ X0 @ X1 @ X2))) = $true))),
% 0.23/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,sK0 @ X0 @ X2 @ X1)],[f13])).
% 0.23/0.31 thf(f17,plain,(
% 0.23/0.31 ! [X3 : 'type/nums/num'] : (($true != (('const/arith/<=' @ X3 @ sK3))) | ((('const/arith/<=' @ sK1 @ X3)) != $true) | ($true = (('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (sK2 @ X3))))) & ((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK3) @ sK2))) != $true)),
% 0.23/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f12])).
% 0.23/0.31 thf(f18,plain,(
% 0.23/0.31 ( ! [X2 : 'type/nums/num',X0 : 'type/nums/num',X1 : 'type/nums/num'] : (($true != (('const/sets/IN' @ 'type/nums/num' @ X1 @ ('const/iterate/..' @ X0 @ X2)))) | ((('const/arith/<=' @ X0 @ X1)) = $true)) )),
% 0.23/0.31 inference(cnf_transformation,[],[f15])).
% 0.23/0.31 thf(f19,plain,(
% 0.23/0.31 ( ! [X2 : 'type/nums/num',X0 : 'type/nums/num',X1 : 'type/nums/num'] : (($true != (('const/sets/IN' @ 'type/nums/num' @ X1 @ ('const/iterate/..' @ X0 @ X2)))) | ($true = (('const/arith/<=' @ X1 @ X2)))) )),
% 0.23/0.31 inference(cnf_transformation,[],[f15])).
% 0.23/0.31 thf(f21,plain,(
% 0.23/0.31 ( ! [X0 : $tType,X2 : (X0 > 'type/realax/real'),X1 : (X0 > $o)] : (($true = (('const/sets/IN' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X1))) | ((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ X0 @ X1 @ X2))) = $true)) )),
% 0.23/0.31 inference(cnf_transformation,[],[f16])).
% 0.23/0.31 thf(f22,plain,(
% 0.23/0.31 ( ! [X0 : $tType,X2 : (X0 > 'type/realax/real'),X1 : (X0 > $o)] : (($true != (('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (X2 @ (sK0 @ X0 @ X2 @ X1))))) | ((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ X0 @ X1 @ X2))) = $true)) )),
% 0.23/0.31 inference(cnf_transformation,[],[f16])).
% 0.23/0.31 thf(f23,plain,(
% 0.23/0.31 ((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK1 @ sK3) @ sK2))) != $true)),
% 0.23/0.31 inference(cnf_transformation,[],[f17])).
% 0.23/0.31 thf(f24,plain,(
% 0.23/0.31 ( ! [X3 : 'type/nums/num'] : (($true = (('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ (sK2 @ X3)))) | ((('const/arith/<=' @ sK1 @ X3)) != $true) | ($true != (('const/arith/<=' @ X3 @ sK3)))) )),
% 0.23/0.31 inference(cnf_transformation,[],[f17])).
% 0.23/0.31 thf(f28,plain,(
% 0.23/0.31 ( ! [X2 : 'type/nums/num',X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num'] : (($true != $true) | ((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0))) = $true) | ($true = (('const/arith/<=' @ (sK0 @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ X1 @ X2)) @ X2)))) )),
% 0.23/0.31 inference(superposition,[],[f19,f21])).
% 0.23/0.31 thf(f29,plain,(
% 0.23/0.31 ( ! [X2 : 'type/nums/num',X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num'] : (((('const/arith/<=' @ X1 @ (sK0 @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ X1 @ X2)))) = $true) | ((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0))) = $true) | ($true != $true)) )),
% 0.23/0.31 inference(superposition,[],[f18,f21])).
% 0.23/0.31 thf(f30,plain,(
% 0.23/0.31 ( ! [X2 : 'type/nums/num',X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num'] : (((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0))) = $true) | ($true = (('const/arith/<=' @ (sK0 @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ X1 @ X2)) @ X2)))) )),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f28])).
% 0.23/0.31 thf(f31,plain,(
% 0.23/0.31 ( ! [X2 : 'type/nums/num',X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num'] : (((('const/arith/<=' @ X1 @ (sK0 @ 'type/nums/num' @ X0 @ ('const/iterate/..' @ X1 @ X2)))) = $true) | ((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0))) = $true)) )),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f29])).
% 0.23/0.31 thf(f32,plain,(
% 0.23/0.31 ( ! [X0 : ('type/nums/num' > $o)] : (($true != (('const/arith/<=' @ (sK0 @ 'type/nums/num' @ sK2 @ X0) @ sK3))) | ($true != (('const/arith/<=' @ sK1 @ (sK0 @ 'type/nums/num' @ sK2 @ X0)))) | ($true != $true) | ((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ 'type/nums/num' @ X0 @ sK2))) = $true)) )),
% 0.23/0.31 inference(superposition,[],[f22,f24])).
% 0.23/0.31 thf(f35,plain,(
% 0.23/0.31 ( ! [X0 : ('type/nums/num' > $o)] : (((('const/realax/real_le' @ ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')) @ ('const/iterate/sum' @ 'type/nums/num' @ X0 @ sK2))) = $true) | ($true != (('const/arith/<=' @ sK1 @ (sK0 @ 'type/nums/num' @ sK2 @ X0)))) | ($true != (('const/arith/<=' @ (sK0 @ 'type/nums/num' @ sK2 @ X0) @ sK3)))) )),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f32])).
% 0.23/0.31 thf(f36,plain,(
% 0.23/0.31 ($true != $true) | ($true != (('const/arith/<=' @ sK1 @ (sK0 @ 'type/nums/num' @ sK2 @ ('const/iterate/..' @ sK1 @ sK3))))) | ((('const/arith/<=' @ (sK0 @ 'type/nums/num' @ sK2 @ ('const/iterate/..' @ sK1 @ sK3)) @ sK3)) != $true)),
% 0.23/0.31 inference(superposition,[],[f23,f35])).
% 0.23/0.31 thf(f37,plain,(
% 0.23/0.31 ((('const/arith/<=' @ (sK0 @ 'type/nums/num' @ sK2 @ ('const/iterate/..' @ sK1 @ sK3)) @ sK3)) != $true) | ($true != (('const/arith/<=' @ sK1 @ (sK0 @ 'type/nums/num' @ sK2 @ ('const/iterate/..' @ sK1 @ sK3)))))),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f36])).
% 0.23/0.31 thf(f38,plain,(
% 0.23/0.31 ((('const/arith/<=' @ (sK0 @ 'type/nums/num' @ sK2 @ ('const/iterate/..' @ sK1 @ sK3)) @ sK3)) = $true) | ($true != $true)),
% 0.23/0.31 inference(superposition,[],[f23,f30])).
% 0.23/0.31 thf(f41,plain,(
% 0.23/0.31 ((('const/arith/<=' @ (sK0 @ 'type/nums/num' @ sK2 @ ('const/iterate/..' @ sK1 @ sK3)) @ sK3)) = $true)),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f38])).
% 0.23/0.31 thf(f42,plain,(
% 0.23/0.31 ($true = (('const/arith/<=' @ sK1 @ (sK0 @ 'type/nums/num' @ sK2 @ ('const/iterate/..' @ sK1 @ sK3))))) | ($true != $true)),
% 0.23/0.31 inference(superposition,[],[f23,f31])).
% 0.23/0.31 thf(f45,plain,(
% 0.23/0.31 ($true = (('const/arith/<=' @ sK1 @ (sK0 @ 'type/nums/num' @ sK2 @ ('const/iterate/..' @ sK1 @ sK3)))))),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f42])).
% 0.23/0.31 thf(f46,plain,(
% 0.23/0.31 ($true != (('const/arith/<=' @ sK1 @ (sK0 @ 'type/nums/num' @ sK2 @ ('const/iterate/..' @ sK1 @ sK3))))) | ($true != $true)),
% 0.23/0.31 inference(superposition,[],[f37,f41])).
% 0.23/0.31 thf(f47,plain,(
% 0.23/0.31 ($true != (('const/arith/<=' @ sK1 @ (sK0 @ 'type/nums/num' @ sK2 @ ('const/iterate/..' @ sK1 @ sK3)))))),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f46])).
% 0.23/0.31 thf(f48,plain,(
% 0.23/0.31 $false),
% 0.23/0.31 inference(forward_subsumption_resolution,[],[f47,f45])).
% 0.23/0.31 % SZS output end Proof for theBenchmark
% 0.23/0.31 % (4176084)------------------------------
% 0.23/0.31 % (4176084)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (4176084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (4176084)CaDiCaL version: 2.1.3
% 0.23/0.31 % (4176084)Termination reason: Refutation
% 0.23/0.31 % (4176084)Time elapsed: 0.007 s
% 0.23/0.31 % (4176084)Peak memory usage: 12 MB
% 0.23/0.31 % (4176084)Instructions burned: 11 (million)
% 0.23/0.31 % (4176075)Success in time 0.043 s
% 0.23/0.31 % Vampire exiting
%------------------------------------------------------------------------------