%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV505^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 08:38:46 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV505^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n017.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 15:50:07 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.29 % (498417)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (498423)lrs+10_16_si=on:nwc=1.5:random_seed=3867772870:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.29 % (498423)Instruction limit reached!
% 0.20/0.29 % (498423)------------------------------
% 0.20/0.29 % (498423)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (498423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (498423)CaDiCaL version: 2.1.3
% 0.20/0.29 % (498423)Termination reason: Instruction limit
% 0.20/0.29 % (498423)Termination phase: Saturation
% 0.20/0.29 % (498423)Time elapsed: 0.006 s
% 0.20/0.29 % (498423)Peak memory usage: 12 MB
% 0.20/0.29 % (498423)Instructions burned: 21 (million)
% 0.20/0.29 % (498422)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3670854110:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.29 % (498424)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=910046926:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.29 % (498424)Instruction limit reached!
% 0.20/0.29 % (498424)------------------------------
% 0.20/0.29 % (498424)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (498424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (498424)CaDiCaL version: 2.1.3
% 0.20/0.29 % (498424)Termination reason: Instruction limit
% 0.20/0.29 % (498424)Termination phase: Saturation
% 0.20/0.29 % (498424)Time elapsed: 0.002 s
% 0.20/0.29 % (498424)Peak memory usage: 11 MB
% 0.20/0.29 % (498424)Instructions burned: 3 (million)
% 0.20/0.29 % (498422) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-498417-498422"...
% 0.20/0.29 % (498430)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1570806269:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.29 % (498422)...printing done.
% 0.20/0.29 % (498430)Instruction limit reached!
% 0.20/0.29 % (498430)------------------------------
% 0.20/0.29 % (498430)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (498430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (498430)CaDiCaL version: 2.1.3
% 0.20/0.29 % (498430)Termination reason: Instruction limit
% 0.20/0.29 % (498430)Termination phase: Saturation
% 0.20/0.29 % (498430)Time elapsed: 0.001 s
% 0.20/0.29 % (498430)Peak memory usage: 11 MB
% 0.20/0.29 % (498430)Instructions burned: 3 (million)
% 0.20/0.29 % (498422)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% 0.20/0.29 thf(type_def_5, type, 'type/nums/num': $tType).
% 0.20/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.29 thf(type_def_7, type, sK0: $tType).
% 0.20/0.29 thf(func_def_0, type, 'const/sets/UNION': !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0 > $o))).
% 0.20/0.29 thf(func_def_1, type, 'const/sets/INTER': !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0 > $o))).
% 0.20/0.29 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.20/0.29 thf(func_def_3, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.29 thf(func_def_4, type, 'const/nums/NUMERAL': ('type/nums/num' > 'type/nums/num')).
% 0.20/0.29 thf(func_def_5, type, 'const/nums/_0': 'type/nums/num').
% 0.20/0.29 thf(func_def_6, type, 'const/iterate/nsum': !>[X0: $tType]:(((X0 > $o) > (X0 > 'type/nums/num') > 'type/nums/num'))).
% 0.20/0.29 thf(func_def_7, type, 'const/iterate/neutral': !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.20/0.29 thf(func_def_8, type, 'const/iterate/monoidal': !>[X0: $tType]:(((X0 > X0 > X0) > $o))).
% 0.20/0.29 thf(func_def_9, type, 'const/iterate/iterate': !>[X0: $tType, X1: $tType]:(((X1 > X1 > X1) > (X0 > $o) > (X0 > X1) > X1))).
% 0.20/0.29 thf(func_def_10, type, 'const/arith/+': ('type/nums/num' > 'type/nums/num' > 'type/nums/num')).
% 0.20/0.29 thf(func_def_14, type, sK1: (sK0 > $o)).
% 0.20/0.29 thf(func_def_15, type, sK2: (sK0 > 'type/nums/num')).
% 0.20/0.29 thf(func_def_16, type, sK3: (sK0 > $o)).
% 0.20/0.29 thf(func_def_17, type, sK4: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > (X0 > $o) > (X1 > X1 > X1) > X0))).
% 0.20/0.29 thf(func_def_18, type, vNOT: ($o > $o)).
% 0.20/0.29 thf(func_def_19, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_20, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.29 thf(f1,axiom,(
% 0.20/0.29 ! [X2 : $tType,X0 : $tType,X1 : (X2 > X2 > X2)] : (('const/iterate/monoidal' @ X2 @ X1) => ! [X4 : (X0 > $o),X3 : (X0 > X2),X5 : (X0 > $o)] : ((! [X6 : X0] : (('const/sets/IN' @ X0 @ X6 @ ('const/sets/INTER' @ X0 @ X4 @ X5)) => (((X3 @ X6)) = (('const/iterate/neutral' @ X2 @ X1)))) & ('const/sets/FINITE' @ X0 @ X5) & ('const/sets/FINITE' @ X0 @ X4)) => ((('const/iterate/iterate' @ X0 @ X2 @ X1 @ ('const/sets/UNION' @ X0 @ X4 @ X5) @ X3)) = ((X1 @ ('const/iterate/iterate' @ X0 @ X2 @ X1 @ X4 @ X3) @ ('const/iterate/iterate' @ X0 @ X2 @ X1 @ X5 @ X3))))))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/ITERATE_UNION_NONZERO_')).
% 0.20/0.29 thf(f2,axiom,(
% 0.20/0.29 ('const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+')),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/MONOIDAL_ADD_')).
% 0.20/0.29 thf(f3,axiom,(
% 0.20/0.29 ! [X0 : $tType] : ('const/iterate/nsum' @ X0 = (('const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+')))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/nsum_')).
% 0.20/0.29 thf(f4,axiom,(
% 0.20/0.29 ((('const/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+')) = (('const/nums/NUMERAL' @ 'const/nums/_0')))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/NEUTRAL_ADD_')).
% 0.20/0.29 thf(f5,conjecture,(
% 0.20/0.29 ! [X0 : $tType,X3 : (X0 > $o),X2 : (X0 > $o),X1 : (X0 > 'type/nums/num')] : ((('const/sets/FINITE' @ X0 @ X3) & ('const/sets/FINITE' @ X0 @ X2) & ! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ ('const/sets/INTER' @ X0 @ X2 @ X3)) => (((X1 @ X4)) = (('const/nums/NUMERAL' @ 'const/nums/_0'))))) => ((('const/iterate/nsum' @ X0 @ ('const/sets/UNION' @ X0 @ X2 @ X3) @ X1)) = (('const/arith/+' @ ('const/iterate/nsum' @ X0 @ X2 @ X1) @ ('const/iterate/nsum' @ X0 @ X3 @ X1)))))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/NSUM_UNION_NONZERO_')).
% 0.20/0.29 thf(f6,negated_conjecture,(
% 0.20/0.29 ~ ! [X0 : $tType,X3 : (X0 > $o),X2 : (X0 > $o),X1 : (X0 > 'type/nums/num')] : ((('const/sets/FINITE' @ X0 @ X3) & ('const/sets/FINITE' @ X0 @ X2) & ! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ ('const/sets/INTER' @ X0 @ X2 @ X3)) => (((X1 @ X4)) = (('const/nums/NUMERAL' @ 'const/nums/_0'))))) => ((('const/iterate/nsum' @ X0 @ ('const/sets/UNION' @ X0 @ X2 @ X3) @ X1)) = (('const/arith/+' @ ('const/iterate/nsum' @ X0 @ X2 @ X1) @ ('const/iterate/nsum' @ X0 @ X3 @ X1)))))),
% 0.20/0.29 inference(negated_conjecture,[status(cth)],[f5])).
% 0.20/0.29 thf(f7,plain,(
% 0.20/0.29 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X0 > X0)] : (('const/iterate/monoidal' @ X0 @ X2) => ! [X3 : (X1 > $o),X4 : (X1 > X0),X5 : (X1 > $o)] : ((! [X6 : X1] : (('const/sets/IN' @ X1 @ X6 @ ('const/sets/INTER' @ X1 @ X3 @ X5)) => ((('const/iterate/neutral' @ X0 @ X2)) = ((X4 @ X6)))) & ('const/sets/FINITE' @ X1 @ X5) & ('const/sets/FINITE' @ X1 @ X3)) => (((X2 @ ('const/iterate/iterate' @ X1 @ X0 @ X2 @ X3 @ X4) @ ('const/iterate/iterate' @ X1 @ X0 @ X2 @ X5 @ X4))) = (('const/iterate/iterate' @ X1 @ X0 @ X2 @ ('const/sets/UNION' @ X1 @ X3 @ X5) @ X4)))))),
% 0.20/0.29 inference(rectify,[],[f1])).
% 0.20/0.29 thf(f8,plain,(
% 0.20/0.29 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X0 > X0)] : (($true = (('const/iterate/monoidal' @ X0 @ X2))) => ! [X4 : (X1 > X0),X5 : (X1 > $o),X3 : (X1 > $o)] : ((((('const/sets/FINITE' @ X1 @ X3)) = $true) & ! [X6 : X1] : (((('const/sets/IN' @ X1 @ X6 @ ('const/sets/INTER' @ X1 @ X3 @ X5))) = $true) => ((('const/iterate/neutral' @ X0 @ X2)) = ((X4 @ X6)))) & ($true = (('const/sets/FINITE' @ X1 @ X5)))) => (((X2 @ ('const/iterate/iterate' @ X1 @ X0 @ X2 @ X3 @ X4) @ ('const/iterate/iterate' @ X1 @ X0 @ X2 @ X5 @ X4))) = (('const/iterate/iterate' @ X1 @ X0 @ X2 @ ('const/sets/UNION' @ X1 @ X3 @ X5) @ X4)))))),
% 0.20/0.29 inference(fool_elimination,[],[f7])).
% 0.20/0.29 thf(f9,plain,(
% 0.20/0.29 ~ ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o),X3 : (X0 > 'type/nums/num')] : ((('const/sets/FINITE' @ X0 @ X1) & ('const/sets/FINITE' @ X0 @ X2) & ! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ ('const/sets/INTER' @ X0 @ X2 @ X1)) => ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((X3 @ X4))))) => ((('const/iterate/nsum' @ X0 @ ('const/sets/UNION' @ X0 @ X2 @ X1) @ X3)) = (('const/arith/+' @ ('const/iterate/nsum' @ X0 @ X2 @ X3) @ ('const/iterate/nsum' @ X0 @ X1 @ X3)))))),
% 0.20/0.29 inference(rectify,[],[f6])).
% 0.20/0.29 thf(f10,plain,(
% 0.20/0.29 ~ ! [X0 : $tType,X1 : (X0 > $o),X3 : (X0 > 'type/nums/num'),X2 : (X0 > $o)] : ((((('const/sets/FINITE' @ X0 @ X2)) = $true) & ! [X4 : X0] : (((('const/sets/IN' @ X0 @ X4 @ ('const/sets/INTER' @ X0 @ X2 @ X1))) = $true) => ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((X3 @ X4)))) & ((('const/sets/FINITE' @ X0 @ X1)) = $true)) => ((('const/iterate/nsum' @ X0 @ ('const/sets/UNION' @ X0 @ X2 @ X1) @ X3)) = (('const/arith/+' @ ('const/iterate/nsum' @ X0 @ X2 @ X3) @ ('const/iterate/nsum' @ X0 @ X1 @ X3)))))),
% 0.20/0.29 inference(fool_elimination,[],[f9])).
% 0.20/0.29 thf(f11,plain,(
% 0.20/0.29 ('const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+')),
% 0.20/0.29 inference(rectify,[],[f2])).
% 0.20/0.29 thf(f12,plain,(
% 0.20/0.29 ((('const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+')) = $true)),
% 0.20/0.29 inference(fool_elimination,[],[f11])).
% 0.20/0.29 thf(f13,plain,(
% 0.20/0.29 ? [X0 : $tType,X1 : (X0 > $o),X3 : (X0 > 'type/nums/num'),X2 : (X0 > $o)] : (((('const/iterate/nsum' @ X0 @ ('const/sets/UNION' @ X0 @ X2 @ X1) @ X3)) != (('const/arith/+' @ ('const/iterate/nsum' @ X0 @ X2 @ X3) @ ('const/iterate/nsum' @ X0 @ X1 @ X3)))) & (((('const/sets/FINITE' @ X0 @ X2)) = $true) & ! [X4 : X0] : (((('const/sets/IN' @ X0 @ X4 @ ('const/sets/INTER' @ X0 @ X2 @ X1))) != $true) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((X3 @ X4)))) & ((('const/sets/FINITE' @ X0 @ X1)) = $true)))),
% 0.20/0.29 inference(ennf_transformation,[],[f10])).
% 0.20/0.29 thf(f14,plain,(
% 0.20/0.29 ? [X0 : $tType,X1 : (X0 > $o),X3 : (X0 > 'type/nums/num'),X2 : (X0 > $o)] : (((('const/iterate/nsum' @ X0 @ ('const/sets/UNION' @ X0 @ X2 @ X1) @ X3)) != (('const/arith/+' @ ('const/iterate/nsum' @ X0 @ X2 @ X3) @ ('const/iterate/nsum' @ X0 @ X1 @ X3)))) & ((('const/sets/FINITE' @ X0 @ X1)) = $true) & ! [X4 : X0] : (((('const/sets/IN' @ X0 @ X4 @ ('const/sets/INTER' @ X0 @ X2 @ X1))) != $true) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((X3 @ X4)))) & ((('const/sets/FINITE' @ X0 @ X2)) = $true))),
% 0.20/0.29 inference(flattening,[],[f13])).
% 0.20/0.29 thf(f15,plain,(
% 0.20/0.29 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X0 > X0)] : (! [X4 : (X1 > X0),X5 : (X1 > $o),X3 : (X1 > $o)] : ((((X2 @ ('const/iterate/iterate' @ X1 @ X0 @ X2 @ X3 @ X4) @ ('const/iterate/iterate' @ X1 @ X0 @ X2 @ X5 @ X4))) = (('const/iterate/iterate' @ X1 @ X0 @ X2 @ ('const/sets/UNION' @ X1 @ X3 @ X5) @ X4))) | (((('const/sets/FINITE' @ X1 @ X3)) != $true) | ? [X6 : X1] : (((('const/sets/IN' @ X1 @ X6 @ ('const/sets/INTER' @ X1 @ X3 @ X5))) = $true) & ((('const/iterate/neutral' @ X0 @ X2)) != ((X4 @ X6)))) | ($true != (('const/sets/FINITE' @ X1 @ X5))))) | ($true != (('const/iterate/monoidal' @ X0 @ X2))))),
% 0.20/0.29 inference(ennf_transformation,[],[f8])).
% 0.20/0.29 thf(f16,plain,(
% 0.20/0.29 ! [X1 : $tType,X0 : $tType,X2 : (X0 > X0 > X0)] : (! [X3 : (X1 > $o),X5 : (X1 > $o),X4 : (X1 > X0)] : ((((X2 @ ('const/iterate/iterate' @ X1 @ X0 @ X2 @ X3 @ X4) @ ('const/iterate/iterate' @ X1 @ X0 @ X2 @ X5 @ X4))) = (('const/iterate/iterate' @ X1 @ X0 @ X2 @ ('const/sets/UNION' @ X1 @ X3 @ X5) @ X4))) | ? [X6 : X1] : (((('const/sets/IN' @ X1 @ X6 @ ('const/sets/INTER' @ X1 @ X3 @ X5))) = $true) & ((('const/iterate/neutral' @ X0 @ X2)) != ((X4 @ X6)))) | ((('const/sets/FINITE' @ X1 @ X3)) != $true) | ($true != (('const/sets/FINITE' @ X1 @ X5)))) | ($true != (('const/iterate/monoidal' @ X0 @ X2))))),
% 0.20/0.29 inference(flattening,[],[f15])).
% 0.20/0.29 thf(f17,plain,(
% 0.20/0.29 ? [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > 'type/nums/num'),X3 : (X0 > $o)] : (((('const/arith/+' @ ('const/iterate/nsum' @ X0 @ X3 @ X2) @ ('const/iterate/nsum' @ X0 @ X1 @ X2))) != (('const/iterate/nsum' @ X0 @ ('const/sets/UNION' @ X0 @ X3 @ X1) @ X2))) & ((('const/sets/FINITE' @ X0 @ X1)) = $true) & ! [X4 : X0] : (((('const/sets/IN' @ X0 @ X4 @ ('const/sets/INTER' @ X0 @ X3 @ X1))) != $true) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((X2 @ X4)))) & ((('const/sets/FINITE' @ X0 @ X3)) = $true))),
% 0.20/0.29 inference(rectify,[],[f14])).
% 0.20/0.29 thf(f18,plain,(
% 0.20/0.29 ((('const/iterate/nsum' @ sK0 @ ('const/sets/UNION' @ sK0 @ sK3 @ sK1) @ sK2)) != (('const/arith/+' @ ('const/iterate/nsum' @ sK0 @ sK3 @ sK2) @ ('const/iterate/nsum' @ sK0 @ sK1 @ sK2)))) & ((('const/sets/FINITE' @ sK0 @ sK1)) = $true) & ! [X4 : sK0] : (($true != (('const/sets/IN' @ sK0 @ X4 @ ('const/sets/INTER' @ sK0 @ sK3 @ sK1)))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK2 @ X4)))) & ((('const/sets/FINITE' @ sK0 @ sK3)) = $true)),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f17])).
% 0.20/0.29 thf(f19,plain,(
% 0.20/0.29 ! [X0 : $tType,X1 : $tType,X2 : (X1 > X1 > X1)] : (! [X3 : (X0 > $o),X4 : (X0 > $o),X5 : (X0 > X1)] : (((('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/UNION' @ X0 @ X3 @ X4) @ X5)) = ((X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X5)))) | ? [X6 : X0] : (((('const/sets/IN' @ X0 @ X6 @ ('const/sets/INTER' @ X0 @ X3 @ X4))) = $true) & ((('const/iterate/neutral' @ X1 @ X2)) != ((X5 @ X6)))) | ((('const/sets/FINITE' @ X0 @ X3)) != $true) | ((('const/sets/FINITE' @ X0 @ X4)) != $true)) | ((('const/iterate/monoidal' @ X1 @ X2)) != $true))),
% 0.20/0.29 inference(rectify,[],[f16])).
% 0.20/0.29 thf(f20,plain,(
% 0.20/0.29 ! [X0 : $tType,X1 : $tType,X2 : (X1 > X1 > X1)] : (! [X3 : (X0 > $o),X4 : (X0 > $o),X5 : (X0 > X1)] : (((('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/UNION' @ X0 @ X3 @ X4) @ X5)) = ((X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X5)))) | (((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) @ ('const/sets/INTER' @ X0 @ X3 @ X4))) = $true) & (((X5 @ (sK4 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2))) != (('const/iterate/neutral' @ X1 @ X2)))) | ((('const/sets/FINITE' @ X0 @ X3)) != $true) | ((('const/sets/FINITE' @ X0 @ X4)) != $true)) | ((('const/iterate/monoidal' @ X1 @ X2)) != $true))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X6,sK4 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2)],[f19])).
% 0.20/0.29 thf(f21,plain,(
% 0.20/0.29 ((('const/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+')) = (('const/nums/NUMERAL' @ 'const/nums/_0')))),
% 0.20/0.29 inference(cnf_transformation,[],[f4])).
% 0.20/0.29 thf(f22,plain,(
% 0.20/0.29 ((('const/sets/FINITE' @ sK0 @ sK3)) = $true)),
% 0.20/0.29 inference(cnf_transformation,[],[f18])).
% 0.20/0.29 thf(f23,plain,(
% 0.20/0.29 ( ! [X4 : sK0] : (($true != (('const/sets/IN' @ sK0 @ X4 @ ('const/sets/INTER' @ sK0 @ sK3 @ sK1)))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK2 @ X4)))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f18])).
% 0.20/0.29 thf(f24,plain,(
% 0.20/0.29 ((('const/sets/FINITE' @ sK0 @ sK1)) = $true)),
% 0.20/0.29 inference(cnf_transformation,[],[f18])).
% 0.20/0.29 thf(f25,plain,(
% 0.20/0.29 ((('const/iterate/nsum' @ sK0 @ ('const/sets/UNION' @ sK0 @ sK3 @ sK1) @ sK2)) != (('const/arith/+' @ ('const/iterate/nsum' @ sK0 @ sK3 @ sK2) @ ('const/iterate/nsum' @ sK0 @ sK1 @ sK2))))),
% 0.20/0.29 inference(cnf_transformation,[],[f18])).
% 0.20/0.29 thf(f26,plain,(
% 0.20/0.29 ((('const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+')) = $true)),
% 0.20/0.29 inference(cnf_transformation,[],[f12])).
% 0.20/0.29 thf(f27,plain,(
% 0.20/0.29 ( ! [X1 : $tType,X0 : $tType,X2 : (X1 > X1 > X1),X3 : (X0 > $o),X4 : (X0 > $o),X5 : (X0 > X1)] : ((((X5 @ (sK4 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2))) != (('const/iterate/neutral' @ X1 @ X2))) | ((('const/sets/FINITE' @ X0 @ X4)) != $true) | ((('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/UNION' @ X0 @ X3 @ X4) @ X5)) = ((X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X5)))) | ((('const/iterate/monoidal' @ X1 @ X2)) != $true) | ((('const/sets/FINITE' @ X0 @ X3)) != $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f20])).
% 0.20/0.29 thf(f28,plain,(
% 0.20/0.29 ( ! [X1 : $tType,X0 : $tType,X2 : (X1 > X1 > X1),X3 : (X0 > $o),X4 : (X0 > $o),X5 : (X0 > X1)] : (((('const/iterate/monoidal' @ X1 @ X2)) != $true) | ((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X1 @ X5 @ X4 @ X3 @ X2) @ ('const/sets/INTER' @ X0 @ X3 @ X4))) = $true) | ((('const/sets/FINITE' @ X0 @ X4)) != $true) | ((('const/sets/FINITE' @ X0 @ X3)) != $true) | ((('const/iterate/iterate' @ X0 @ X1 @ X2 @ ('const/sets/UNION' @ X0 @ X3 @ X4) @ X5)) = ((X2 @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ X5) @ ('const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X5))))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f20])).
% 0.20/0.29 thf(f29,plain,(
% 0.20/0.29 ( ! [X0 : $tType] : (('const/iterate/nsum' @ X0 = (('const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+')))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f3])).
% 0.20/0.29 thf(f32,plain,(
% 0.20/0.29 ((('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ ('const/sets/UNION' @ sK0 @ sK3 @ sK1) @ sK2)) != (('const/arith/+' @ ('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK3 @ sK2) @ ('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK1 @ sK2))))),
% 0.20/0.29 inference(definition_unfolding,[],[f25,f29,f29,f29])).
% 0.20/0.29 thf(f35,plain,(
% 0.20/0.29 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : (X0 > $o),X1 : (X0 > 'type/nums/num')] : (((('const/sets/FINITE' @ X0 @ X2)) != $true) | ($true = (('const/sets/IN' @ X0 @ (sK4 @ X0 @ 'type/nums/num' @ X1 @ X2 @ X3 @ 'const/arith/+') @ ('const/sets/INTER' @ X0 @ X3 @ X2)))) | ($true != $true) | ((('const/sets/FINITE' @ X0 @ X3)) != $true) | ((('const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+' @ ('const/sets/UNION' @ X0 @ X3 @ X2) @ X1)) = (('const/arith/+' @ ('const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+' @ X3 @ X1) @ ('const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+' @ X2 @ X1))))) )),
% 0.20/0.29 inference(constrained_superposition,[],[f28,f26])).
% 0.20/0.29 thf(f36,plain,(
% 0.20/0.29 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : (X0 > $o),X1 : (X0 > 'type/nums/num')] : (((('const/sets/FINITE' @ X0 @ X3)) != $true) | ((('const/sets/FINITE' @ X0 @ X2)) != $true) | ((('const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+' @ ('const/sets/UNION' @ X0 @ X3 @ X2) @ X1)) = (('const/arith/+' @ ('const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+' @ X3 @ X1) @ ('const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+' @ X2 @ X1)))) | ($true = (('const/sets/IN' @ X0 @ (sK4 @ X0 @ 'type/nums/num' @ X1 @ X2 @ X3 @ 'const/arith/+') @ ('const/sets/INTER' @ X0 @ X3 @ X2))))) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f35])).
% 0.20/0.29 thf(f37,plain,(
% 0.20/0.29 ( ! [X0 : (sK0 > $o),X1 : (sK0 > 'type/nums/num')] : (($true != (('const/sets/FINITE' @ sK0 @ X0))) | ((('const/arith/+' @ ('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK3 @ X1) @ ('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ X0 @ X1))) = (('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ ('const/sets/UNION' @ sK0 @ sK3 @ X0) @ X1))) | ((('const/sets/IN' @ sK0 @ (sK4 @ sK0 @ 'type/nums/num' @ X1 @ X0 @ sK3 @ 'const/arith/+') @ ('const/sets/INTER' @ sK0 @ sK3 @ X0))) = $true) | ($true != $true)) )),
% 0.20/0.29 inference(constrained_superposition,[],[f36,f22])).
% 0.20/0.29 thf(f40,plain,(
% 0.20/0.29 ( ! [X0 : (sK0 > $o),X1 : (sK0 > 'type/nums/num')] : (($true != (('const/sets/FINITE' @ sK0 @ X0))) | ((('const/arith/+' @ ('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK3 @ X1) @ ('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ X0 @ X1))) = (('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ ('const/sets/UNION' @ sK0 @ sK3 @ X0) @ X1))) | ((('const/sets/IN' @ sK0 @ (sK4 @ sK0 @ 'type/nums/num' @ X1 @ X0 @ sK3 @ 'const/arith/+') @ ('const/sets/INTER' @ sK0 @ sK3 @ X0))) = $true)) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f37])).
% 0.20/0.29 thf(f46,plain,(
% 0.20/0.29 ( ! [X0 : (sK0 > 'type/nums/num')] : (($true != $true) | ((('const/sets/IN' @ sK0 @ (sK4 @ sK0 @ 'type/nums/num' @ X0 @ sK1 @ sK3 @ 'const/arith/+') @ ('const/sets/INTER' @ sK0 @ sK3 @ sK1))) = $true) | ((('const/arith/+' @ ('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK3 @ X0) @ ('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK1 @ X0))) = (('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ ('const/sets/UNION' @ sK0 @ sK3 @ sK1) @ X0)))) )),
% 0.20/0.29 inference(constrained_superposition,[],[f40,f24])).
% 0.20/0.29 thf(f48,plain,(
% 0.20/0.29 ( ! [X0 : (sK0 > 'type/nums/num')] : (((('const/arith/+' @ ('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK3 @ X0) @ ('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK1 @ X0))) = (('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ ('const/sets/UNION' @ sK0 @ sK3 @ sK1) @ X0))) | ((('const/sets/IN' @ sK0 @ (sK4 @ sK0 @ 'type/nums/num' @ X0 @ sK1 @ sK3 @ 'const/arith/+') @ ('const/sets/INTER' @ sK0 @ sK3 @ sK1))) = $true)) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f46])).
% 0.20/0.29 thf(f49,plain,(
% 0.20/0.29 ( ! [X0 : (sK0 > 'type/nums/num')] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK2 @ (sK4 @ sK0 @ 'type/nums/num' @ X0 @ sK1 @ sK3 @ 'const/arith/+')))) | ($true != $true) | ((('const/arith/+' @ ('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK3 @ X0) @ ('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK1 @ X0))) = (('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ ('const/sets/UNION' @ sK0 @ sK3 @ sK1) @ X0)))) )),
% 0.20/0.29 inference(constrained_superposition,[],[f23,f48])).
% 0.20/0.29 thf(f50,plain,(
% 0.20/0.29 ( ! [X0 : (sK0 > 'type/nums/num')] : (((('const/arith/+' @ ('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK3 @ X0) @ ('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK1 @ X0))) = (('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ ('const/sets/UNION' @ sK0 @ sK3 @ sK1) @ X0))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK2 @ (sK4 @ sK0 @ 'type/nums/num' @ X0 @ sK1 @ sK3 @ 'const/arith/+'))))) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f49])).
% 0.20/0.29 thf(f51,plain,(
% 0.20/0.29 ((('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ ('const/sets/UNION' @ sK0 @ sK3 @ sK1) @ sK2)) != (('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ ('const/sets/UNION' @ sK0 @ sK3 @ sK1) @ sK2))) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK2 @ (sK4 @ sK0 @ 'type/nums/num' @ sK2 @ sK1 @ sK3 @ 'const/arith/+'))))),
% 0.20/0.29 inference(constrained_superposition,[],[f32,f50])).
% 0.20/0.29 thf(f52,plain,(
% 0.20/0.29 ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((sK2 @ (sK4 @ sK0 @ 'type/nums/num' @ sK2 @ sK1 @ sK3 @ 'const/arith/+'))))),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f51])).
% 0.20/0.29 thf(f53,plain,(
% 0.20/0.29 ((('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ ('const/sets/UNION' @ sK0 @ sK3 @ sK1) @ sK2)) = (('const/arith/+' @ ('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK3 @ sK2) @ ('const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK1 @ sK2)))) | ((('const/sets/FINITE' @ sK0 @ sK1)) != $true) | ((('const/sets/FINITE' @ sK0 @ sK3)) != $true) | ((('const/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+')) != (('const/nums/NUMERAL' @ 'const/nums/_0'))) | ((('const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+')) != $true)),
% 0.20/0.29 inference(constrained_superposition,[],[f27,f52])).
% 0.20/0.29 thf(f54,plain,(
% 0.20/0.29 ((('const/sets/FINITE' @ sK0 @ sK1)) != $true) | ((('const/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+')) != (('const/nums/NUMERAL' @ 'const/nums/_0'))) | ((('const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+')) != $true) | ((('const/sets/FINITE' @ sK0 @ sK3)) != $true)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f53,f32])).
% 0.20/0.29 thf(f55,plain,(
% 0.20/0.29 ((('const/sets/FINITE' @ sK0 @ sK3)) != $true) | ((('const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+')) != $true) | ((('const/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+')) != (('const/nums/NUMERAL' @ 'const/nums/_0')))),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f54,f24])).
% 0.20/0.29 thf(f56,plain,(
% 0.20/0.29 ((('const/iterate/neutral' @ 'type/nums/num' @ 'const/arith/+')) != (('const/nums/NUMERAL' @ 'const/nums/_0'))) | ((('const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+')) != $true)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f55,f22])).
% 0.20/0.29 thf(f57,plain,(
% 0.20/0.29 ((('const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+')) != $true)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f56,f21])).
% 0.20/0.29 thf(f58,plain,(
% 0.20/0.29 $false),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f57,f26])).
% 0.20/0.29 % SZS output end Proof for theBenchmark
% 0.20/0.29 % (498422)------------------------------
% 0.20/0.29 % (498422)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (498422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (498422)CaDiCaL version: 2.1.3
% 0.20/0.29 % (498422)Termination reason: Refutation
% 0.20/0.29 % (498422)Time elapsed: 0.009 s
% 0.20/0.29 % (498422)Peak memory usage: 12 MB
% 0.20/0.29 % (498422)Instructions burned: 16 (million)
% 0.20/0.29 % (498417)Success in time 0.046 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------