%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV504^1 : 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 : n016.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 08:38:45 AM UTC 2026
% Result : Theorem 0.23s 0.29s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV504^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n016.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 15:59:34 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.23/0.29 % (520745)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.29 % (520753)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=322701260: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)
% 0.23/0.29 % (520754)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1099765591:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.29 % (520750)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1013747914:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.29 % (520751)lrs+10_16_si=on:nwc=1.5:random_seed=1560190748:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.29 % (520752)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3112152364:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.29 % (520752)Instruction limit reached!
% 0.23/0.29 % (520752)------------------------------
% 0.23/0.29 % (520752)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (520752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (520752)CaDiCaL version: 2.1.3
% 0.23/0.29 % (520752)Termination reason: Instruction limit
% 0.23/0.29 % (520752)Termination phase: Saturation
% 0.23/0.29 % (520752)Time elapsed: 0.003 s
% 0.23/0.29 % (520752)Peak memory usage: 12 MB
% 0.23/0.29 % (520752)Instructions burned: 3 (million)
% 0.23/0.29 % (520756)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.29 % (520756)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
% 0.23/0.29 % (520753) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-520745-520753"...
% 0.23/0.29 % (520756)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=4262108844:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.29 % (520753)...printing done.
% 0.23/0.29 % (520753)Refutation found. Thanks to Tanya!
% 0.23/0.29 % SZS status Theorem for theBenchmark
% 0.23/0.29 % SZS output start Proof for theBenchmark
% 0.23/0.29 thf(type_def_5, type, 'type/nums/num': $tType).
% 0.23/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.29 thf(type_def_7, type, sK0: $tType).
% 0.23/0.29 thf(func_def_0, type, 'const/sets/SUBSET': !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 0.23/0.29 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.23/0.29 thf(func_def_2, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.23/0.29 thf(func_def_3, type, 'const/sets/DIFF': !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0 > $o))).
% 0.23/0.29 thf(func_def_4, type, 'const/nums/NUMERAL': ('type/nums/num' > 'type/nums/num')).
% 0.23/0.29 thf(func_def_5, type, 'const/nums/_0': 'type/nums/num').
% 0.23/0.29 thf(func_def_6, type, 'const/iterate/nsum': !>[X0: $tType]:(((X0 > $o) > (X0 > 'type/nums/num') > 'type/nums/num'))).
% 0.23/0.29 thf(func_def_7, type, 'const/arith/<=': ('type/nums/num' > 'type/nums/num' > $o)).
% 0.23/0.29 thf(func_def_11, type, sK1: (sK0 > 'type/nums/num')).
% 0.23/0.29 thf(func_def_12, type, sK2: (sK0 > $o)).
% 0.23/0.29 thf(func_def_13, type, sK3: (sK0 > $o)).
% 0.23/0.29 thf(func_def_14, type, sK4: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > 'type/nums/num') > X0))).
% 0.23/0.29 thf(func_def_15, type, sK5: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.23/0.29 thf(f1,axiom,(
% 0.23/0.29 ! [X0 : $tType,X3 : (X0 > 'type/nums/num'),X1 : (X0 > $o),X2 : (X0 > $o)] : ((('const/sets/FINITE' @ X0 @ X2) & ! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ ('const/sets/DIFF' @ X0 @ X1 @ X2)) => (((X3 @ X4)) = (('const/nums/NUMERAL' @ 'const/nums/_0')))) & ('const/sets/FINITE' @ X0 @ X1)) => ('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3)))),
% 0.23/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/NSUM_SUBSET_')).
% 0.23/0.29 thf(f2,axiom,(
% 0.23/0.29 ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) & ('const/sets/FINITE' @ X0 @ X2)) => ('const/sets/FINITE' @ X0 @ X1))),
% 0.23/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_SUBSET_')).
% 0.23/0.29 thf(f3,axiom,(
% 0.23/0.29 ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = ! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) => ('const/sets/IN' @ X0 @ X3 @ X2)))),
% 0.23/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUBSET_')).
% 0.23/0.29 thf(f4,axiom,(
% 0.23/0.29 ! [X0 : $tType,X3 : X0,X1 : (X0 > $o),X2 : (X0 > $o)] : (~('const/sets/IN' @ X0 @ X3 @ X2) & ('const/sets/IN' @ X0 @ X3 @ X1) = (('const/sets/IN' @ X0 @ X3 @ ('const/sets/DIFF' @ X0 @ X1 @ X2))))),
% 0.23/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_DIFF_')).
% 0.23/0.29 thf(f5,conjecture,(
% 0.23/0.29 ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o),X3 : (X0 > 'type/nums/num')] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) & ('const/sets/FINITE' @ X0 @ X2)) => ('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3)))),
% 0.23/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/NSUM_SUBSET_SIMPLE_')).
% 0.23/0.29 thf(f6,negated_conjecture,(
% 0.23/0.29 ~ ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o),X3 : (X0 > 'type/nums/num')] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) & ('const/sets/FINITE' @ X0 @ X2)) => ('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3)))),
% 0.23/0.29 inference(negated_conjecture,[status(cth)],[f5])).
% 0.23/0.29 thf(f7,plain,(
% 0.23/0.29 ! [X0 : $tType,X1 : (X0 > 'type/nums/num'),X2 : (X0 > $o),X3 : (X0 > $o)] : ((('const/sets/FINITE' @ X0 @ X3) & ! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ ('const/sets/DIFF' @ X0 @ X2 @ X3)) => ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((X1 @ X4)))) & ('const/sets/FINITE' @ X0 @ X2)) => ('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X2 @ X1) @ ('const/iterate/nsum' @ X0 @ X3 @ X1)))),
% 0.23/0.29 inference(rectify,[],[f1])).
% 0.23/0.29 thf(f8,plain,(
% 0.23/0.29 ! [X0 : $tType,X1 : (X0 > 'type/nums/num'),X2 : (X0 > $o),X3 : (X0 > $o)] : ((($true = (('const/sets/FINITE' @ X0 @ X3))) & ! [X4 : X0] : (($true = (('const/sets/IN' @ X0 @ X4 @ ('const/sets/DIFF' @ X0 @ X2 @ X3)))) => ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((X1 @ X4)))) & ((('const/sets/FINITE' @ X0 @ X2)) = $true)) => ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X2 @ X1) @ ('const/iterate/nsum' @ X0 @ X3 @ X1)))))),
% 0.23/0.29 inference(fool_elimination,[],[f7])).
% 0.23/0.29 thf(f9,plain,(
% 0.23/0.29 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((('const/sets/SUBSET' @ X0 @ X2 @ X1) & ('const/sets/FINITE' @ X0 @ X1)) => ('const/sets/FINITE' @ X0 @ X2))),
% 0.23/0.29 inference(rectify,[],[f2])).
% 0.23/0.29 thf(f10,plain,(
% 0.23/0.29 ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : ((((('const/sets/SUBSET' @ X0 @ X2 @ X1)) = $true) & ((('const/sets/FINITE' @ X0 @ X1)) = $true)) => ((('const/sets/FINITE' @ X0 @ X2)) = $true))),
% 0.23/0.29 inference(fool_elimination,[],[f9])).
% 0.23/0.29 thf(f11,plain,(
% 0.23/0.29 ~ ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o),X3 : (X0 > 'type/nums/num')] : ((('const/sets/SUBSET' @ X0 @ X2 @ X1) & ('const/sets/FINITE' @ X0 @ X1)) => ('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X2 @ X3) @ ('const/iterate/nsum' @ X0 @ X1 @ X3)))),
% 0.23/0.29 inference(rectify,[],[f6])).
% 0.23/0.29 thf(f12,plain,(
% 0.23/0.29 ~ ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o),X3 : (X0 > 'type/nums/num')] : ((((('const/sets/FINITE' @ X0 @ X1)) = $true) & ((('const/sets/SUBSET' @ X0 @ X2 @ X1)) = $true)) => ((('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X2 @ X3) @ ('const/iterate/nsum' @ X0 @ X1 @ X3))) = $true))),
% 0.23/0.29 inference(fool_elimination,[],[f11])).
% 0.23/0.29 thf(f13,plain,(
% 0.23/0.29 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((('const/sets/SUBSET' @ X0 @ X2 @ X1)) = ! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X2) => ('const/sets/IN' @ X0 @ X3 @ X1)))),
% 0.23/0.29 inference(rectify,[],[f3])).
% 0.23/0.29 thf(f14,plain,(
% 0.23/0.29 ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (! [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X2)) = $true) => ((('const/sets/IN' @ X0 @ X3 @ X1)) = $true)) <=> ((('const/sets/SUBSET' @ X0 @ X2 @ X1)) = $true))),
% 0.23/0.29 inference(fool_elimination,[],[f13])).
% 0.23/0.29 thf(f15,plain,(
% 0.23/0.29 ! [X0 : $tType,X1 : X0,X2 : (X0 > $o),X3 : (X0 > $o)] : (~('const/sets/IN' @ X0 @ X1 @ X3) & ('const/sets/IN' @ X0 @ X1 @ X2) = (('const/sets/IN' @ X0 @ X1 @ ('const/sets/DIFF' @ X0 @ X2 @ X3))))),
% 0.23/0.29 inference(rectify,[],[f4])).
% 0.23/0.29 thf(f16,plain,(
% 0.23/0.29 ! [X0 : $tType,X1 : X0,X2 : (X0 > $o),X3 : (X0 > $o)] : ((~ ($true = (('const/sets/IN' @ X0 @ X1 @ X3))) & ($true = (('const/sets/IN' @ X0 @ X1 @ X2)))) <=> ((('const/sets/IN' @ X0 @ X1 @ ('const/sets/DIFF' @ X0 @ X2 @ X3))) = $true))),
% 0.23/0.29 inference(fool_elimination,[],[f15])).
% 0.23/0.29 thf(f17,plain,(
% 0.23/0.29 ! [X0 : $tType,X2 : (X0 > $o),X3 : (X0 > $o),X1 : X0] : (((('const/sets/IN' @ X0 @ X1 @ ('const/sets/DIFF' @ X0 @ X2 @ X3))) = $true) <=> (($true != (('const/sets/IN' @ X0 @ X1 @ X3))) & ($true = (('const/sets/IN' @ X0 @ X1 @ X2)))))),
% 0.23/0.29 inference(flattening,[],[f16])).
% 0.23/0.29 thf(f18,plain,(
% 0.23/0.29 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (! [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X2)) != $true) | ((('const/sets/IN' @ X0 @ X3 @ X1)) = $true)) <=> ((('const/sets/SUBSET' @ X0 @ X2 @ X1)) = $true))),
% 0.23/0.29 inference(ennf_transformation,[],[f14])).
% 0.23/0.29 thf(f19,plain,(
% 0.23/0.29 ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (((('const/sets/FINITE' @ X0 @ X2)) = $true) | (((('const/sets/SUBSET' @ X0 @ X2 @ X1)) != $true) | ((('const/sets/FINITE' @ X0 @ X1)) != $true)))),
% 0.23/0.29 inference(ennf_transformation,[],[f10])).
% 0.23/0.29 thf(f20,plain,(
% 0.23/0.29 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (((('const/sets/FINITE' @ X0 @ X2)) = $true) | ((('const/sets/FINITE' @ X0 @ X1)) != $true) | ((('const/sets/SUBSET' @ X0 @ X2 @ X1)) != $true))),
% 0.23/0.29 inference(flattening,[],[f19])).
% 0.23/0.29 thf(f21,plain,(
% 0.23/0.29 ? [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o),X3 : (X0 > 'type/nums/num')] : (((('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X2 @ X3) @ ('const/iterate/nsum' @ X0 @ X1 @ X3))) != $true) & (((('const/sets/FINITE' @ X0 @ X1)) = $true) & ((('const/sets/SUBSET' @ X0 @ X2 @ X1)) = $true)))),
% 0.23/0.29 inference(ennf_transformation,[],[f12])).
% 0.23/0.29 thf(f22,plain,(
% 0.23/0.29 ? [X0 : $tType,X3 : (X0 > 'type/nums/num'),X1 : (X0 > $o),X2 : (X0 > $o)] : (((('const/sets/SUBSET' @ X0 @ X2 @ X1)) = $true) & ((('const/sets/FINITE' @ X0 @ X1)) = $true) & ((('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X2 @ X3) @ ('const/iterate/nsum' @ X0 @ X1 @ X3))) != $true))),
% 0.23/0.29 inference(flattening,[],[f21])).
% 0.23/0.29 thf(f23,plain,(
% 0.23/0.29 ! [X0 : $tType,X1 : (X0 > 'type/nums/num'),X2 : (X0 > $o),X3 : (X0 > $o)] : (($true = (('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X2 @ X1) @ ('const/iterate/nsum' @ X0 @ X3 @ X1)))) | (($true != (('const/sets/FINITE' @ X0 @ X3))) | ? [X4 : X0] : (($true = (('const/sets/IN' @ X0 @ X4 @ ('const/sets/DIFF' @ X0 @ X2 @ X3)))) & ((('const/nums/NUMERAL' @ 'const/nums/_0')) != ((X1 @ X4)))) | ((('const/sets/FINITE' @ X0 @ X2)) != $true)))),
% 0.23/0.29 inference(ennf_transformation,[],[f8])).
% 0.23/0.29 thf(f24,plain,(
% 0.23/0.29 ! [X0 : $tType,X1 : (X0 > 'type/nums/num'),X2 : (X0 > $o),X3 : (X0 > $o)] : (($true = (('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X2 @ X1) @ ('const/iterate/nsum' @ X0 @ X3 @ X1)))) | ($true != (('const/sets/FINITE' @ X0 @ X3))) | ? [X4 : X0] : (($true = (('const/sets/IN' @ X0 @ X4 @ ('const/sets/DIFF' @ X0 @ X2 @ X3)))) & ((('const/nums/NUMERAL' @ 'const/nums/_0')) != ((X1 @ X4)))) | ((('const/sets/FINITE' @ X0 @ X2)) != $true))),
% 0.23/0.29 inference(flattening,[],[f23])).
% 0.23/0.29 thf(f25,plain,(
% 0.23/0.29 ? [X0 : $tType,X1 : (X0 > 'type/nums/num'),X2 : (X0 > $o),X3 : (X0 > $o)] : (($true = (('const/sets/SUBSET' @ X0 @ X3 @ X2))) & ((('const/sets/FINITE' @ X0 @ X2)) = $true) & ((('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X3 @ X1) @ ('const/iterate/nsum' @ X0 @ X2 @ X1))) != $true))),
% 0.23/0.29 inference(rectify,[],[f22])).
% 0.23/0.29 thf(f26,plain,(
% 0.23/0.29 ((('const/sets/SUBSET' @ sK0 @ sK3 @ sK2)) = $true) & ((('const/sets/FINITE' @ sK0 @ sK2)) = $true) & ($true != (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK3 @ sK1) @ ('const/iterate/nsum' @ sK0 @ sK2 @ sK1))))),
% 0.23/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f25])).
% 0.23/0.29 thf(f27,plain,(
% 0.23/0.29 ! [X0 : $tType,X2 : (X0 > $o),X3 : (X0 > $o),X1 : X0] : ((((('const/sets/IN' @ X0 @ X1 @ ('const/sets/DIFF' @ X0 @ X2 @ X3))) = $true) | (($true = (('const/sets/IN' @ X0 @ X1 @ X3))) | ($true != (('const/sets/IN' @ X0 @ X1 @ X2))))) & ((($true != (('const/sets/IN' @ X0 @ X1 @ X3))) & ($true = (('const/sets/IN' @ X0 @ X1 @ X2)))) | ((('const/sets/IN' @ X0 @ X1 @ ('const/sets/DIFF' @ X0 @ X2 @ X3))) != $true)))),
% 0.23/0.29 inference(nnf_transformation,[],[f17])).
% 0.23/0.29 thf(f28,plain,(
% 0.23/0.29 ! [X0 : $tType,X2 : (X0 > $o),X3 : (X0 > $o),X1 : X0] : ((((('const/sets/IN' @ X0 @ X1 @ ('const/sets/DIFF' @ X0 @ X2 @ X3))) = $true) | ($true = (('const/sets/IN' @ X0 @ X1 @ X3))) | ($true != (('const/sets/IN' @ X0 @ X1 @ X2)))) & ((($true != (('const/sets/IN' @ X0 @ X1 @ X3))) & ($true = (('const/sets/IN' @ X0 @ X1 @ X2)))) | ((('const/sets/IN' @ X0 @ X1 @ ('const/sets/DIFF' @ X0 @ X2 @ X3))) != $true)))),
% 0.23/0.29 inference(flattening,[],[f27])).
% 0.23/0.29 thf(f29,plain,(
% 0.23/0.29 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o),X3 : X0] : ((((('const/sets/IN' @ X0 @ X3 @ ('const/sets/DIFF' @ X0 @ X1 @ X2))) = $true) | ((('const/sets/IN' @ X0 @ X3 @ X2)) = $true) | ((('const/sets/IN' @ X0 @ X3 @ X1)) != $true)) & ((((('const/sets/IN' @ X0 @ X3 @ X2)) != $true) & ((('const/sets/IN' @ X0 @ X3 @ X1)) = $true)) | ((('const/sets/IN' @ X0 @ X3 @ ('const/sets/DIFF' @ X0 @ X1 @ X2))) != $true)))),
% 0.23/0.29 inference(rectify,[],[f28])).
% 0.23/0.29 thf(f30,plain,(
% 0.23/0.29 ! [X0 : $tType,X1 : (X0 > 'type/nums/num'),X2 : (X0 > $o),X3 : (X0 > $o)] : (($true = (('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X2 @ X1) @ ('const/iterate/nsum' @ X0 @ X3 @ X1)))) | ($true != (('const/sets/FINITE' @ X0 @ X3))) | (((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X3 @ X2 @ X1) @ ('const/sets/DIFF' @ X0 @ X2 @ X3))) = $true) & ((('const/nums/NUMERAL' @ 'const/nums/_0')) != ((X1 @ (sK4 @ X0 @ X3 @ X2 @ X1))))) | ((('const/sets/FINITE' @ X0 @ X2)) != $true))),
% 0.23/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,sK4 @ X0 @ X3 @ X2 @ X1)],[f24])).
% 0.23/0.29 thf(f31,plain,(
% 0.23/0.29 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((! [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X2)) != $true) | ((('const/sets/IN' @ X0 @ X3 @ X1)) = $true)) | ((('const/sets/SUBSET' @ X0 @ X2 @ X1)) != $true)) & (((('const/sets/SUBSET' @ X0 @ X2 @ X1)) = $true) | ? [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X2)) = $true) & ((('const/sets/IN' @ X0 @ X3 @ X1)) != $true))))),
% 0.23/0.29 inference(nnf_transformation,[],[f18])).
% 0.23/0.29 thf(f32,plain,(
% 0.23/0.29 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((! [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X2)) != $true) | ((('const/sets/IN' @ X0 @ X3 @ X1)) = $true)) | ((('const/sets/SUBSET' @ X0 @ X2 @ X1)) != $true)) & (((('const/sets/SUBSET' @ X0 @ X2 @ X1)) = $true) | ? [X4 : X0] : (((('const/sets/IN' @ X0 @ X4 @ X2)) = $true) & ($true != (('const/sets/IN' @ X0 @ X4 @ X1))))))),
% 0.23/0.29 inference(rectify,[],[f31])).
% 0.23/0.29 thf(f33,plain,(
% 0.23/0.29 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((! [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X2)) != $true) | ((('const/sets/IN' @ X0 @ X3 @ X1)) = $true)) | ((('const/sets/SUBSET' @ X0 @ X2 @ X1)) != $true)) & (((('const/sets/SUBSET' @ X0 @ X2 @ X1)) = $true) | (($true = (('const/sets/IN' @ X0 @ (sK5 @ X0 @ X2 @ X1) @ X2))) & ($true != (('const/sets/IN' @ X0 @ (sK5 @ X0 @ X2 @ X1) @ X1))))))),
% 0.23/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,sK4 @ X0 @ X3 @ X2 @ X1)],[f32])).
% 0.23/0.29 thf(f34,plain,(
% 0.23/0.29 ($true != (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK3 @ sK1) @ ('const/iterate/nsum' @ sK0 @ sK2 @ sK1))))),
% 0.23/0.29 inference(cnf_transformation,[],[f26])).
% 0.23/0.29 thf(f35,plain,(
% 0.23/0.29 ((('const/sets/FINITE' @ sK0 @ sK2)) = $true)),
% 0.23/0.29 inference(cnf_transformation,[],[f26])).
% 0.23/0.29 thf(f36,plain,(
% 0.23/0.29 ((('const/sets/SUBSET' @ sK0 @ sK3 @ sK2)) = $true)),
% 0.23/0.29 inference(cnf_transformation,[],[f26])).
% 0.23/0.29 thf(f37,plain,(
% 0.23/0.29 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : X0,X1 : (X0 > $o)] : (((('const/sets/IN' @ X0 @ X3 @ ('const/sets/DIFF' @ X0 @ X1 @ X2))) != $true) | ((('const/sets/IN' @ X0 @ X3 @ X1)) = $true)) )),
% 0.23/0.29 inference(cnf_transformation,[],[f29])).
% 0.23/0.29 thf(f38,plain,(
% 0.23/0.29 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : X0,X1 : (X0 > $o)] : (((('const/sets/IN' @ X0 @ X3 @ ('const/sets/DIFF' @ X0 @ X1 @ X2))) != $true) | ((('const/sets/IN' @ X0 @ X3 @ X2)) != $true)) )),
% 0.23/0.29 inference(cnf_transformation,[],[f29])).
% 0.23/0.29 thf(f40,plain,(
% 0.23/0.29 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (((('const/sets/SUBSET' @ X0 @ X2 @ X1)) != $true) | ((('const/sets/FINITE' @ X0 @ X1)) != $true) | ((('const/sets/FINITE' @ X0 @ X2)) = $true)) )),
% 0.23/0.29 inference(cnf_transformation,[],[f20])).
% 0.23/0.29 thf(f42,plain,(
% 0.23/0.29 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : (X0 > $o),X1 : (X0 > 'type/nums/num')] : (((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X3 @ X2 @ X1) @ ('const/sets/DIFF' @ X0 @ X2 @ X3))) = $true) | ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X2 @ X1) @ ('const/iterate/nsum' @ X0 @ X3 @ X1)))) | ($true != (('const/sets/FINITE' @ X0 @ X3))) | ((('const/sets/FINITE' @ X0 @ X2)) != $true)) )),
% 0.23/0.29 inference(cnf_transformation,[],[f30])).
% 0.23/0.29 thf(f45,plain,(
% 0.23/0.29 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : X0,X1 : (X0 > $o)] : (((('const/sets/SUBSET' @ X0 @ X2 @ X1)) != $true) | ((('const/sets/IN' @ X0 @ X3 @ X2)) != $true) | ((('const/sets/IN' @ X0 @ X3 @ X1)) = $true)) )),
% 0.23/0.29 inference(cnf_transformation,[],[f33])).
% 0.23/0.29 thf(f48,definition,(
% 0.23/0.29 spl6_1 <=> ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK3 @ sK1) @ ('const/iterate/nsum' @ sK0 @ sK2 @ sK1))))),
% 0.23/0.29 introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
% 0.23/0.29 thf(f50,plain,(
% 0.23/0.29 ($true != (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK3 @ sK1) @ ('const/iterate/nsum' @ sK0 @ sK2 @ sK1)))) | spl6_1),
% 0.23/0.29 inference(avatar_component_clause,[],[f48])).
% 0.23/0.29 thf(f51,plain,(
% 0.23/0.29 ~spl6_1),
% 0.23/0.29 inference(avatar_split_clause,[],[f34,f48])).
% 0.23/0.29 thf(f53,definition,(
% 0.23/0.29 spl6_2 <=> ((('const/sets/FINITE' @ sK0 @ sK2)) = $true)),
% 0.23/0.29 introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
% 0.23/0.29 thf(f55,plain,(
% 0.23/0.29 ((('const/sets/FINITE' @ sK0 @ sK2)) = $true) | ~spl6_2),
% 0.23/0.29 inference(avatar_component_clause,[],[f53])).
% 0.23/0.29 thf(f56,plain,(
% 0.23/0.29 spl6_2),
% 0.23/0.29 inference(avatar_split_clause,[],[f35,f53])).
% 0.23/0.29 thf(f58,definition,(
% 0.23/0.29 spl6_3 <=> ((('const/sets/SUBSET' @ sK0 @ sK3 @ sK2)) = $true)),
% 0.23/0.29 introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition])).
% 0.23/0.29 thf(f60,plain,(
% 0.23/0.29 ((('const/sets/SUBSET' @ sK0 @ sK3 @ sK2)) = $true) | ~spl6_3),
% 0.23/0.29 inference(avatar_component_clause,[],[f58])).
% 0.23/0.29 thf(f61,plain,(
% 0.23/0.29 spl6_3),
% 0.23/0.29 inference(avatar_split_clause,[],[f36,f58])).
% 0.23/0.29 thf(f62,plain,(
% 0.23/0.29 ($true = (('const/sets/FINITE' @ sK0 @ sK3))) | ((('const/sets/FINITE' @ sK0 @ sK2)) != $true) | ($true != $true) | ~spl6_3),
% 0.23/0.29 inference(superposition,[],[f40,f60])).
% 0.23/0.29 thf(f63,plain,(
% 0.23/0.29 ($true = (('const/sets/FINITE' @ sK0 @ sK3))) | ((('const/sets/FINITE' @ sK0 @ sK2)) != $true) | ~spl6_3),
% 0.23/0.29 inference(trivial_inequality_removal,[],[f62])).
% 0.23/0.29 thf(f64,plain,(
% 0.23/0.29 ($true = (('const/sets/FINITE' @ sK0 @ sK3))) | (~spl6_2 | ~spl6_3)),
% 0.23/0.29 inference(forward_subsumption_resolution,[],[f63,f55])).
% 0.23/0.29 thf(f66,definition,(
% 0.23/0.29 spl6_4 <=> ($true = (('const/sets/FINITE' @ sK0 @ sK3)))),
% 0.23/0.29 introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition])).
% 0.23/0.29 thf(f68,plain,(
% 0.23/0.29 ($true = (('const/sets/FINITE' @ sK0 @ sK3))) | ~spl6_4),
% 0.23/0.29 inference(avatar_component_clause,[],[f66])).
% 0.23/0.29 thf(f69,plain,(
% 0.23/0.29 spl6_4 | ~spl6_2 | ~spl6_3),
% 0.23/0.29 inference(avatar_split_clause,[],[f64,f58,f53,f66])).
% 0.23/0.29 thf(f75,plain,(
% 0.23/0.29 ( ! [X0 : sK0] : (($true = (('const/sets/IN' @ sK0 @ X0 @ sK2))) | ($true != (('const/sets/IN' @ sK0 @ X0 @ sK3))) | ($true != $true)) ) | ~spl6_3),
% 0.23/0.29 inference(superposition,[],[f45,f60])).
% 0.23/0.29 thf(f76,plain,(
% 0.23/0.29 ( ! [X0 : sK0] : (($true = (('const/sets/IN' @ sK0 @ X0 @ sK2))) | ($true != (('const/sets/IN' @ sK0 @ X0 @ sK3)))) ) | ~spl6_3),
% 0.23/0.29 inference(trivial_inequality_removal,[],[f75])).
% 0.23/0.29 thf(f83,plain,(
% 0.23/0.29 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : (X0 > 'type/nums/num'),X1 : (X0 > $o)] : (((('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X2 @ X3) @ ('const/iterate/nsum' @ X0 @ X1 @ X3))) = $true) | ($true != $true) | ((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X1 @ X2 @ X3) @ X2)) = $true) | ((('const/sets/FINITE' @ X0 @ X2)) != $true) | ((('const/sets/FINITE' @ X0 @ X1)) != $true)) )),
% 0.23/0.29 inference(superposition,[],[f37,f42])).
% 0.23/0.29 thf(f84,plain,(
% 0.23/0.29 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : (X0 > 'type/nums/num'),X1 : (X0 > $o)] : (((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X1 @ X2 @ X3) @ X1)) != $true) | ($true != $true) | ((('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X2 @ X3) @ ('const/iterate/nsum' @ X0 @ X1 @ X3))) = $true) | ((('const/sets/FINITE' @ X0 @ X2)) != $true) | ((('const/sets/FINITE' @ X0 @ X1)) != $true)) )),
% 0.23/0.29 inference(superposition,[],[f38,f42])).
% 0.23/0.29 thf(f85,plain,(
% 0.23/0.29 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : (X0 > 'type/nums/num'),X1 : (X0 > $o)] : (((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X1 @ X2 @ X3) @ X1)) != $true) | ((('const/sets/FINITE' @ X0 @ X2)) != $true) | ((('const/sets/FINITE' @ X0 @ X1)) != $true) | ((('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X2 @ X3) @ ('const/iterate/nsum' @ X0 @ X1 @ X3))) = $true)) )),
% 0.23/0.29 inference(trivial_inequality_removal,[],[f84])).
% 0.23/0.29 thf(f86,plain,(
% 0.23/0.29 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : (X0 > 'type/nums/num'),X1 : (X0 > $o)] : (((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X1 @ X2 @ X3) @ X2)) = $true) | ((('const/sets/FINITE' @ X0 @ X2)) != $true) | ((('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X2 @ X3) @ ('const/iterate/nsum' @ X0 @ X1 @ X3))) = $true) | ((('const/sets/FINITE' @ X0 @ X1)) != $true)) )),
% 0.23/0.30 inference(trivial_inequality_removal,[],[f83])).
% 0.23/0.30 thf(f114,plain,(
% 0.23/0.30 ( ! [X0 : (sK0 > $o),X1 : (sK0 > 'type/nums/num')] : (($true != (('const/sets/IN' @ sK0 @ (sK4 @ sK0 @ sK2 @ X0 @ X1) @ sK3))) | ($true != $true) | ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ X0 @ X1) @ ('const/iterate/nsum' @ sK0 @ sK2 @ X1)))) | ($true != (('const/sets/FINITE' @ sK0 @ X0))) | ((('const/sets/FINITE' @ sK0 @ sK2)) != $true)) ) | ~spl6_3),
% 0.23/0.30 inference(superposition,[],[f85,f76])).
% 0.23/0.30 thf(f116,plain,(
% 0.23/0.30 ( ! [X0 : (sK0 > $o),X1 : (sK0 > 'type/nums/num')] : (((('const/sets/FINITE' @ sK0 @ sK2)) != $true) | ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ X0 @ X1) @ ('const/iterate/nsum' @ sK0 @ sK2 @ X1)))) | ($true != (('const/sets/FINITE' @ sK0 @ X0))) | ($true != (('const/sets/IN' @ sK0 @ (sK4 @ sK0 @ sK2 @ X0 @ X1) @ sK3)))) ) | ~spl6_3),
% 0.23/0.30 inference(trivial_inequality_removal,[],[f114])).
% 0.23/0.30 thf(f118,plain,(
% 0.23/0.30 ( ! [X0 : (sK0 > $o),X1 : (sK0 > 'type/nums/num')] : (($true != (('const/sets/IN' @ sK0 @ (sK4 @ sK0 @ sK2 @ X0 @ X1) @ sK3))) | ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ X0 @ X1) @ ('const/iterate/nsum' @ sK0 @ sK2 @ X1)))) | ($true != (('const/sets/FINITE' @ sK0 @ X0)))) ) | (~spl6_2 | ~spl6_3)),
% 0.23/0.30 inference(forward_subsumption_resolution,[],[f116,f55])).
% 0.23/0.30 thf(f150,plain,(
% 0.23/0.30 ( ! [X0 : (sK0 > 'type/nums/num')] : (((('const/sets/FINITE' @ sK0 @ sK2)) != $true) | ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK3 @ X0) @ ('const/iterate/nsum' @ sK0 @ sK2 @ X0)))) | ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK3 @ X0) @ ('const/iterate/nsum' @ sK0 @ sK2 @ X0)))) | ($true != (('const/sets/FINITE' @ sK0 @ sK3))) | ($true != $true) | ($true != (('const/sets/FINITE' @ sK0 @ sK3)))) ) | (~spl6_2 | ~spl6_3)),
% 0.23/0.30 inference(superposition,[],[f118,f86])).
% 0.23/0.30 thf(f151,plain,(
% 0.23/0.30 ( ! [X0 : (sK0 > 'type/nums/num')] : (((('const/sets/FINITE' @ sK0 @ sK2)) != $true) | ($true != (('const/sets/FINITE' @ sK0 @ sK3))) | ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK3 @ X0) @ ('const/iterate/nsum' @ sK0 @ sK2 @ X0)))) | ($true != $true)) ) | (~spl6_2 | ~spl6_3)),
% 0.23/0.30 inference(duplicate_literal_removal,[],[f150])).
% 0.23/0.30 thf(f152,plain,(
% 0.23/0.30 ( ! [X0 : (sK0 > 'type/nums/num')] : (($true != (('const/sets/FINITE' @ sK0 @ sK3))) | ((('const/sets/FINITE' @ sK0 @ sK2)) != $true) | ($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK3 @ X0) @ ('const/iterate/nsum' @ sK0 @ sK2 @ X0))))) ) | (~spl6_2 | ~spl6_3)),
% 0.23/0.30 inference(trivial_inequality_removal,[],[f151])).
% 0.23/0.30 thf(f153,plain,(
% 0.23/0.30 ( ! [X0 : (sK0 > 'type/nums/num')] : (($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK3 @ X0) @ ('const/iterate/nsum' @ sK0 @ sK2 @ X0)))) | ((('const/sets/FINITE' @ sK0 @ sK2)) != $true)) ) | (~spl6_2 | ~spl6_3 | ~spl6_4)),
% 0.23/0.30 inference(forward_subsumption_resolution,[],[f152,f68])).
% 0.23/0.30 thf(f154,plain,(
% 0.23/0.30 ( ! [X0 : (sK0 > 'type/nums/num')] : (($true = (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK3 @ X0) @ ('const/iterate/nsum' @ sK0 @ sK2 @ X0))))) ) | (~spl6_2 | ~spl6_3 | ~spl6_4)),
% 0.23/0.30 inference(forward_subsumption_resolution,[],[f153,f55])).
% 0.23/0.30 thf(f286,plain,(
% 0.23/0.30 ($true != $true) | (spl6_1 | ~spl6_2 | ~spl6_3 | ~spl6_4)),
% 0.23/0.30 inference(superposition,[],[f50,f154])).
% 0.23/0.30 thf(f287,plain,(
% 0.23/0.30 $false | (spl6_1 | ~spl6_2 | ~spl6_3 | ~spl6_4)),
% 0.23/0.30 inference(trivial_inequality_removal,[],[f286])).
% 0.23/0.30 thf(f288,plain,(
% 0.23/0.30 spl6_1 | ~spl6_2 | ~spl6_3 | ~spl6_4),
% 0.23/0.30 inference(avatar_contradiction_clause,[],[f287])).
% 0.23/0.30 cnf(s1, plain, ~spl6_1, inference(sat_conversion,[],[f51])).
% 0.23/0.30 cnf(s2, plain, spl6_2, inference(sat_conversion,[],[f56])).
% 0.23/0.30 cnf(s3, plain, spl6_3, inference(sat_conversion,[],[f61])).
% 0.23/0.30 cnf(s4, plain, ~spl6_2 | ~spl6_3 | spl6_4, inference(sat_conversion,[],[f69])).
% 0.23/0.30 cnf(s6, plain, spl6_1 | ~spl6_2 | ~spl6_3 | ~spl6_4, inference(sat_conversion,[],[f288])).
% 0.23/0.30 cnf(s7, plain, spl6_4, inference(rat,[],[s4,s3,s2])).
% 0.23/0.30 cnf(s8, plain, spl6_1, inference(rat,[],[s6,s2,s3,s7])).
% 0.23/0.30 cnf(s9, plain, $false, inference(rat,[],[s1,s8])).
% 0.23/0.30 thf(f289,plain,(
% 0.23/0.30 $false),
% 0.23/0.30 inference(avatar_sat_refutation,[],[s9])).
% 0.23/0.30 % SZS output end Proof for theBenchmark
% 0.23/0.30 % (520753)------------------------------
% 0.23/0.30 % (520753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (520753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (520753)CaDiCaL version: 2.1.3
% 0.23/0.30 % (520753)Termination reason: Refutation
% 0.23/0.30 % (520753)Time elapsed: 0.016 s
% 0.23/0.30 % (520753)Peak memory usage: 13 MB
% 0.23/0.30 % (520753)Instructions burned: 45 (million)
% 0.23/0.30 % (520745)Success in time 0.042 s
% 0.23/0.30 % Vampire exiting
%------------------------------------------------------------------------------