%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN048^1 : 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 : n006.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 08:19:55 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 : NUN048^1 : 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 : n006.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 13:06:55 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.20/0.29 % (682874)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (682883)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3071034600:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.29 % (682885)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.29 % (682885)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
% 0.20/0.29 % (682883)Instruction limit reached!
% 0.20/0.29 % (682883)------------------------------
% 0.20/0.29 % (682883)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (682883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (682883)CaDiCaL version: 2.1.3
% 0.20/0.29 % (682883)Termination reason: Instruction limit
% 0.20/0.29 % (682883)Termination phase: Saturation
% 0.20/0.29 % (682883)Time elapsed: 0.007 s
% 0.20/0.29 % (682883)Peak memory usage: 12 MB
% 0.20/0.29 % (682883)Instructions burned: 27 (million)
% 0.20/0.29 % (682879)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3899932653:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.29 % (682880)lrs+10_16_si=on:nwc=1.5:random_seed=131036144:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.29 % (682882)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=1850235903: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)
% 0.20/0.29 % (682881)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=121462199:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.29 % (682885)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=3710750295:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.29 % (682884)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3452797935:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.29 % (682881)Instruction limit reached!
% 0.20/0.29 % (682881)------------------------------
% 0.20/0.29 % (682881)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (682881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (682881)CaDiCaL version: 2.1.3
% 0.20/0.29 % (682881)Termination reason: Instruction limit
% 0.20/0.29 % (682881)Termination phase: Saturation
% 0.20/0.29 % (682881)Time elapsed: 0.003 s
% 0.20/0.29 % (682881)Peak memory usage: 12 MB
% 0.20/0.29 % (682881)Instructions burned: 4 (million)
% 0.20/0.29 % (682882) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-682874-682882"...
% 0.20/0.29 % (682882)...printing done.
% 0.20/0.29 % (682882)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(func_def_0, type, 'const/trivia/I': !>[X0: $tType]:((X0 > X0))).
% 0.20/0.29 thf(func_def_1, type, 'const/nums/NUMERAL': ('type/nums/num' > 'type/nums/num')).
% 0.20/0.29 thf(func_def_2, type, 'const/nums/_0': 'type/nums/num').
% 0.20/0.29 thf(func_def_3, type, 'const/iterate/nsum': !>[X0: $tType]:(((X0 > $o) > (X0 > 'type/nums/num') > 'type/nums/num'))).
% 0.20/0.29 thf(func_def_4, type, 'const/iterate/..': ('type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o)).
% 0.20/0.29 thf(func_def_5, type, 'const/arith/<=': ('type/nums/num' > 'type/nums/num' > $o)).
% 0.20/0.29 thf(func_def_6, type, 'const/arith/<': ('type/nums/num' > 'type/nums/num' > $o)).
% 0.20/0.29 thf(func_def_10, type, sK0: 'type/nums/num').
% 0.20/0.29 thf(func_def_11, type, sK1: 'type/nums/num').
% 0.20/0.29 thf(func_def_12, type, sK2: ('type/nums/num' > 'type/nums/num')).
% 0.20/0.29 thf(func_def_13, type, sK3: (('type/nums/num' > 'type/nums/num') > 'type/nums/num' > 'type/nums/num' > 'type/nums/num')).
% 0.20/0.29 thf(f2,axiom,(
% 0.20/0.29 ! [X1 : 'type/nums/num',X0 : 'type/nums/num'] : (~('const/arith/<' @ X0 @ X1) = (('const/arith/<=' @ X1 @ X0)))),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/arith/NOT_LT_')).
% 0.20/0.29 thf(f3,axiom,(
% 0.20/0.29 ! [X0 : 'type/nums/num',X2 : 'type/nums/num',X1 : 'type/nums/num'] : ((('const/arith/<=' @ X1 @ X2) & ('const/arith/<=' @ X0 @ X1)) => ('const/arith/<=' @ X0 @ X2))),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/arith/LE_TRANS_')).
% 0.20/0.29 thf(f4,axiom,(
% 0.20/0.29 ! [X1 : 'type/nums/num',X2 : 'type/nums/num',X0 : ('type/nums/num' > 'type/nums/num')] : (! [X3 : 'type/nums/num'] : ((('const/arith/<=' @ X3 @ X2) & ('const/arith/<=' @ X1 @ X3)) => (((X0 @ X3)) = (('const/nums/NUMERAL' @ 'const/nums/_0')))) => ((('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)) = (('const/nums/NUMERAL' @ 'const/nums/_0'))))),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/NSUM_EQ_0_NUMSEG_')).
% 0.20/0.29 thf(f5,conjecture,(
% 0.20/0.29 ! [X2 : 'type/nums/num',X0 : ('type/nums/num' > 'type/nums/num'),X1 : 'type/nums/num'] : (('const/arith/<' @ X2 @ X1) => ((('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)) = (('const/nums/NUMERAL' @ 'const/nums/_0'))))),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/NSUM_TRIV_NUMSEG_')).
% 0.20/0.29 thf(f6,negated_conjecture,(
% 0.20/0.29 ~ ! [X2 : 'type/nums/num',X0 : ('type/nums/num' > 'type/nums/num'),X1 : 'type/nums/num'] : (('const/arith/<' @ X2 @ X1) => ((('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)) = (('const/nums/NUMERAL' @ 'const/nums/_0'))))),
% 0.20/0.29 inference(negated_conjecture,[status(cth)],[f5])).
% 0.20/0.29 thf(f7,plain,(
% 0.20/0.29 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : ((('const/arith/<=' @ X2 @ X1) & ('const/arith/<=' @ X0 @ X2)) => ('const/arith/<=' @ X0 @ X1))),
% 0.20/0.29 inference(rectify,[],[f3])).
% 0.20/0.29 thf(f8,plain,(
% 0.20/0.29 ! [X2 : 'type/nums/num',X1 : 'type/nums/num',X0 : 'type/nums/num'] : ((((('const/arith/<=' @ X0 @ X2)) = $true) & ($true = (('const/arith/<=' @ X2 @ X1)))) => ((('const/arith/<=' @ X0 @ X1)) = $true))),
% 0.20/0.29 inference(fool_elimination,[],[f7])).
% 0.20/0.29 thf(f9,plain,(
% 0.20/0.29 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (~('const/arith/<' @ X1 @ X0) = (('const/arith/<=' @ X0 @ X1)))),
% 0.20/0.29 inference(rectify,[],[f2])).
% 0.20/0.29 thf(f10,plain,(
% 0.20/0.29 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (~ ((('const/arith/<' @ X1 @ X0)) = $true) <=> ((('const/arith/<=' @ X0 @ X1)) = $true))),
% 0.20/0.29 inference(fool_elimination,[],[f9])).
% 0.20/0.29 thf(f11,plain,(
% 0.20/0.29 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : ('type/nums/num' > 'type/nums/num')] : (! [X3 : 'type/nums/num'] : ((('const/arith/<=' @ X3 @ X1) & ('const/arith/<=' @ X0 @ X3)) => ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((X2 @ X3)))) => ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2))))),
% 0.20/0.29 inference(rectify,[],[f4])).
% 0.20/0.29 thf(f12,plain,(
% 0.20/0.29 ! [X2 : ('type/nums/num' > 'type/nums/num'),X1 : 'type/nums/num',X0 : 'type/nums/num'] : (! [X3 : 'type/nums/num'] : ((((('const/arith/<=' @ X3 @ X1)) = $true) & ((('const/arith/<=' @ X0 @ X3)) = $true)) => ((('const/nums/NUMERAL' @ 'const/nums/_0')) = ((X2 @ X3)))) => ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2))))),
% 0.20/0.29 inference(fool_elimination,[],[f11])).
% 0.20/0.29 thf(f13,plain,(
% 0.20/0.29 ~ ! [X0 : 'type/nums/num',X1 : ('type/nums/num' > 'type/nums/num'),X2 : 'type/nums/num'] : (('const/arith/<' @ X0 @ X2) => ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X2 @ X0) @ X1))))),
% 0.20/0.29 inference(rectify,[],[f6])).
% 0.20/0.29 thf(f14,plain,(
% 0.20/0.29 ~ ! [X1 : ('type/nums/num' > 'type/nums/num'),X2 : 'type/nums/num',X0 : 'type/nums/num'] : (($true = (('const/arith/<' @ X0 @ X2))) => ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X2 @ X0) @ X1))))),
% 0.20/0.29 inference(fool_elimination,[],[f13])).
% 0.20/0.29 thf(f15,plain,(
% 0.20/0.29 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/arith/<=' @ X0 @ X1)) = $true) <=> ((('const/arith/<' @ X1 @ X0)) != $true))),
% 0.20/0.29 inference(flattening,[],[f10])).
% 0.20/0.29 thf(f16,plain,(
% 0.20/0.29 ! [X2 : 'type/nums/num',X1 : 'type/nums/num',X0 : 'type/nums/num'] : (((('const/arith/<=' @ X0 @ X1)) = $true) | (((('const/arith/<=' @ X0 @ X2)) != $true) | ($true != (('const/arith/<=' @ X2 @ X1)))))),
% 0.20/0.29 inference(ennf_transformation,[],[f8])).
% 0.20/0.29 thf(f17,plain,(
% 0.20/0.29 ! [X1 : 'type/nums/num',X2 : 'type/nums/num',X0 : 'type/nums/num'] : (((('const/arith/<=' @ X0 @ X1)) = $true) | ($true != (('const/arith/<=' @ X2 @ X1))) | ((('const/arith/<=' @ X0 @ X2)) != $true))),
% 0.20/0.29 inference(flattening,[],[f16])).
% 0.20/0.29 thf(f18,plain,(
% 0.20/0.29 ? [X2 : 'type/nums/num',X0 : 'type/nums/num',X1 : ('type/nums/num' > 'type/nums/num')] : (($true = (('const/arith/<' @ X0 @ X2))) & ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X2 @ X0) @ X1))))),
% 0.20/0.29 inference(ennf_transformation,[],[f14])).
% 0.20/0.29 thf(f19,plain,(
% 0.20/0.29 ! [X2 : ('type/nums/num' > 'type/nums/num'),X1 : 'type/nums/num',X0 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2))) | ? [X3 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) != ((X2 @ X3))) & (((('const/arith/<=' @ X3 @ X1)) = $true) & ((('const/arith/<=' @ X0 @ X3)) = $true))))),
% 0.20/0.29 inference(ennf_transformation,[],[f12])).
% 0.20/0.29 thf(f20,plain,(
% 0.20/0.29 ! [X1 : 'type/nums/num',X0 : 'type/nums/num',X2 : ('type/nums/num' > 'type/nums/num')] : (? [X3 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) != ((X2 @ X3))) & ((('const/arith/<=' @ X3 @ X1)) = $true) & ((('const/arith/<=' @ X0 @ X3)) = $true)) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2))))),
% 0.20/0.29 inference(flattening,[],[f19])).
% 0.20/0.29 thf(f21,plain,(
% 0.20/0.29 ? [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : ('type/nums/num' > 'type/nums/num')] : (((('const/arith/<' @ X1 @ X0)) = $true) & ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2))))),
% 0.20/0.29 inference(rectify,[],[f18])).
% 0.20/0.29 thf(f22,plain,(
% 0.20/0.29 ((('const/arith/<' @ sK1 @ sK0)) = $true) & ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK0 @ sK1) @ sK2)))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f21])).
% 0.20/0.29 thf(f23,plain,(
% 0.20/0.29 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : (($true = (('const/arith/<=' @ X2 @ X0))) | ((('const/arith/<=' @ X1 @ X0)) != $true) | ($true != (('const/arith/<=' @ X2 @ X1))))),
% 0.20/0.29 inference(rectify,[],[f17])).
% 0.20/0.29 thf(f24,plain,(
% 0.20/0.29 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ((((('const/arith/<=' @ X0 @ X1)) = $true) | ((('const/arith/<' @ X1 @ X0)) = $true)) & (((('const/arith/<' @ X1 @ X0)) != $true) | ((('const/arith/<=' @ X0 @ X1)) != $true)))),
% 0.20/0.29 inference(nnf_transformation,[],[f15])).
% 0.20/0.29 thf(f25,plain,(
% 0.20/0.29 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : ('type/nums/num' > 'type/nums/num')] : (? [X3 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) != ((X2 @ X3))) & ($true = (('const/arith/<=' @ X3 @ X0))) & ((('const/arith/<=' @ X1 @ X3)) = $true)) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X0) @ X2))))),
% 0.20/0.29 inference(rectify,[],[f20])).
% 0.20/0.29 thf(f26,plain,(
% 0.20/0.29 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : ('type/nums/num' > 'type/nums/num')] : ((((('const/nums/NUMERAL' @ 'const/nums/_0')) != ((X2 @ (sK3 @ X2 @ X1 @ X0)))) & ($true = (('const/arith/<=' @ (sK3 @ X2 @ X1 @ X0) @ X0))) & ((('const/arith/<=' @ X1 @ (sK3 @ X2 @ X1 @ X0))) = $true)) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X0) @ X2))))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,sK3 @ X2 @ X1 @ X0)],[f25])).
% 0.20/0.29 thf(f28,plain,(
% 0.20/0.29 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK0 @ sK1) @ sK2)))),
% 0.20/0.29 inference(cnf_transformation,[],[f22])).
% 0.20/0.29 thf(f29,plain,(
% 0.20/0.29 ((('const/arith/<' @ sK1 @ sK0)) = $true)),
% 0.20/0.29 inference(cnf_transformation,[],[f22])).
% 0.20/0.29 thf(f30,plain,(
% 0.20/0.29 ( ! [X2 : 'type/nums/num',X0 : 'type/nums/num',X1 : 'type/nums/num'] : (($true = (('const/arith/<=' @ X2 @ X0))) | ($true != (('const/arith/<=' @ X2 @ X1))) | ((('const/arith/<=' @ X1 @ X0)) != $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f23])).
% 0.20/0.29 thf(f31,plain,(
% 0.20/0.29 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/arith/<' @ X1 @ X0)) != $true) | ((('const/arith/<=' @ X0 @ X1)) != $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f24])).
% 0.20/0.29 thf(f33,plain,(
% 0.20/0.29 ( ! [X2 : ('type/nums/num' > 'type/nums/num'),X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X0) @ X2))) | ((('const/arith/<=' @ X1 @ (sK3 @ X2 @ X1 @ X0))) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f26])).
% 0.20/0.29 thf(f34,plain,(
% 0.20/0.29 ( ! [X2 : ('type/nums/num' > 'type/nums/num'),X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X0) @ X2))) | ($true = (('const/arith/<=' @ (sK3 @ X2 @ X1 @ X0) @ X0)))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f26])).
% 0.20/0.29 thf(f38,definition,(
% 0.20/0.29 spl4_1 <=> ((('const/nums/NUMERAL' @ 'const/nums/_0')) = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK0 @ sK1) @ sK2)))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.20/0.29 thf(f40,plain,(
% 0.20/0.29 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK0 @ sK1) @ sK2))) | spl4_1),
% 0.20/0.29 inference(avatar_component_clause,[],[f38])).
% 0.20/0.29 thf(f41,plain,(
% 0.20/0.29 ~spl4_1),
% 0.20/0.29 inference(avatar_split_clause,[],[f28,f38])).
% 0.20/0.29 thf(f43,definition,(
% 0.20/0.29 spl4_2 <=> ((('const/arith/<' @ sK1 @ sK0)) = $true)),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.20/0.29 thf(f45,plain,(
% 0.20/0.29 ((('const/arith/<' @ sK1 @ sK0)) = $true) | ~spl4_2),
% 0.20/0.29 inference(avatar_component_clause,[],[f43])).
% 0.20/0.29 thf(f46,plain,(
% 0.20/0.29 spl4_2),
% 0.20/0.29 inference(avatar_split_clause,[],[f29,f43])).
% 0.20/0.29 thf(f48,plain,(
% 0.20/0.29 ($true != (('const/arith/<=' @ sK0 @ sK1))) | ($true != $true) | ~spl4_2),
% 0.20/0.29 inference(superposition,[],[f31,f45])).
% 0.20/0.29 thf(f50,plain,(
% 0.20/0.29 ($true != (('const/arith/<=' @ sK0 @ sK1))) | ~spl4_2),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f48])).
% 0.20/0.29 thf(f52,definition,(
% 0.20/0.29 spl4_3 <=> ($true = (('const/arith/<=' @ sK0 @ sK1)))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])).
% 0.20/0.29 thf(f54,plain,(
% 0.20/0.29 ($true != (('const/arith/<=' @ sK0 @ sK1))) | spl4_3),
% 0.20/0.29 inference(avatar_component_clause,[],[f52])).
% 0.20/0.29 thf(f55,plain,(
% 0.20/0.29 ~spl4_3 | ~spl4_2),
% 0.20/0.29 inference(avatar_split_clause,[],[f50,f43,f52])).
% 0.20/0.29 thf(f56,plain,(
% 0.20/0.29 ( ! [X0 : 'type/nums/num'] : (($true != (('const/arith/<=' @ sK0 @ X0))) | ($true != (('const/arith/<=' @ X0 @ sK1))) | ($true != $true)) ) | spl4_3),
% 0.20/0.29 inference(superposition,[],[f54,f30])).
% 0.20/0.29 thf(f57,plain,(
% 0.20/0.29 ( ! [X0 : 'type/nums/num'] : (($true != (('const/arith/<=' @ sK0 @ X0))) | ($true != (('const/arith/<=' @ X0 @ sK1)))) ) | spl4_3),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f56])).
% 0.20/0.29 thf(f58,plain,(
% 0.20/0.29 ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/nums/NUMERAL' @ 'const/nums/_0'))) | ((('const/arith/<=' @ sK0 @ (sK3 @ sK2 @ sK0 @ sK1))) = $true) | spl4_1),
% 0.20/0.29 inference(superposition,[],[f40,f33])).
% 0.20/0.29 thf(f59,plain,(
% 0.20/0.29 ((('const/arith/<=' @ sK0 @ (sK3 @ sK2 @ sK0 @ sK1))) = $true) | spl4_1),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f58])).
% 0.20/0.29 thf(f61,definition,(
% 0.20/0.29 spl4_4 <=> ((('const/arith/<=' @ sK0 @ (sK3 @ sK2 @ sK0 @ sK1))) = $true)),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition])).
% 0.20/0.29 thf(f63,plain,(
% 0.20/0.29 ((('const/arith/<=' @ sK0 @ (sK3 @ sK2 @ sK0 @ sK1))) = $true) | ~spl4_4),
% 0.20/0.29 inference(avatar_component_clause,[],[f61])).
% 0.20/0.29 thf(f64,plain,(
% 0.20/0.29 spl4_4 | spl4_1),
% 0.20/0.29 inference(avatar_split_clause,[],[f59,f38,f61])).
% 0.20/0.29 thf(f65,plain,(
% 0.20/0.29 ((('const/arith/<=' @ (sK3 @ sK2 @ sK0 @ sK1) @ sK1)) = $true) | ((('const/nums/NUMERAL' @ 'const/nums/_0')) != (('const/nums/NUMERAL' @ 'const/nums/_0'))) | spl4_1),
% 0.20/0.29 inference(superposition,[],[f40,f34])).
% 0.20/0.29 thf(f66,plain,(
% 0.20/0.29 ((('const/arith/<=' @ (sK3 @ sK2 @ sK0 @ sK1) @ sK1)) = $true) | spl4_1),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f65])).
% 0.20/0.29 thf(f68,definition,(
% 0.20/0.29 spl4_5 <=> ((('const/arith/<=' @ (sK3 @ sK2 @ sK0 @ sK1) @ sK1)) = $true)),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition])).
% 0.20/0.29 thf(f71,plain,(
% 0.20/0.29 spl4_5 | spl4_1),
% 0.20/0.29 inference(avatar_split_clause,[],[f66,f38,f68])).
% 0.20/0.29 thf(f76,plain,(
% 0.20/0.29 ($true != $true) | ((('const/arith/<=' @ (sK3 @ sK2 @ sK0 @ sK1) @ sK1)) != $true) | (spl4_3 | ~spl4_4)),
% 0.20/0.29 inference(superposition,[],[f57,f63])).
% 0.20/0.29 thf(f77,plain,(
% 0.20/0.29 ((('const/arith/<=' @ (sK3 @ sK2 @ sK0 @ sK1) @ sK1)) != $true) | (spl4_3 | ~spl4_4)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f76])).
% 0.20/0.29 thf(f78,plain,(
% 0.20/0.29 ~spl4_5 | spl4_3 | ~spl4_4),
% 0.20/0.29 inference(avatar_split_clause,[],[f77,f61,f52,f68])).
% 0.20/0.29 cnf(s1, plain, ~spl4_1, inference(sat_conversion,[],[f41])).
% 0.20/0.29 cnf(s2, plain, spl4_2, inference(sat_conversion,[],[f46])).
% 0.20/0.29 cnf(s3, plain, ~spl4_2 | ~spl4_3, inference(sat_conversion,[],[f55])).
% 0.20/0.29 cnf(s4, plain, spl4_1 | spl4_4, inference(sat_conversion,[],[f64])).
% 0.20/0.29 cnf(s5, plain, spl4_1 | spl4_5, inference(sat_conversion,[],[f71])).
% 0.20/0.29 cnf(s6, plain, spl4_3 | ~spl4_4 | ~spl4_5, inference(sat_conversion,[],[f78])).
% 0.20/0.29 cnf(s7, plain, ~spl4_3, inference(rat,[],[s3,s2])).
% 0.20/0.29 cnf(s8, plain, spl4_5, inference(rat,[],[s5,s1])).
% 0.20/0.29 cnf(s9, plain, spl4_4, inference(rat,[],[s4,s1])).
% 0.20/0.29 cnf(s10, plain, $false, inference(rat,[],[s6,s7,s8,s9])).
% 0.20/0.29 thf(f79,plain,(
% 0.20/0.29 $false),
% 0.20/0.29 inference(avatar_sat_refutation,[],[s10])).
% 0.20/0.29 % SZS output end Proof for theBenchmark
% 0.20/0.29 % (682882)------------------------------
% 0.20/0.29 % (682882)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (682882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (682882)CaDiCaL version: 2.1.3
% 0.20/0.29 % (682882)Termination reason: Refutation
% 0.20/0.29 % (682882)Time elapsed: 0.006 s
% 0.20/0.29 % (682882)Peak memory usage: 13 MB
% 0.20/0.29 % (682882)Instructions burned: 8 (million)
% 0.20/0.29 % (682874)Success in time 0.043 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------