%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA108^1 : 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 07:45:56 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA108^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n006.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 17:44:31 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.21/0.30 % (1077862)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.30 % (1077871)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3500733680:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.30 % (1077873)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.30 % (1077873)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
% 0.21/0.30 % (1077871)Instruction limit reached!
% 0.21/0.30 % (1077871)------------------------------
% 0.21/0.30 % (1077871)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (1077871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (1077871)CaDiCaL version: 2.1.3
% 0.21/0.30 % (1077871)Termination reason: Instruction limit
% 0.21/0.30 % (1077871)Termination phase: Saturation
% 0.21/0.30 % (1077871)Time elapsed: 0.007 s
% 0.21/0.30 % (1077871)Peak memory usage: 12 MB
% 0.21/0.30 % (1077871)Instructions burned: 25 (million)
% 0.21/0.30 % (1077868)lrs+10_16_si=on:nwc=1.5:random_seed=901918628:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.30 % (1077869)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3275695594:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.30 % (1077867)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=798715127:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.30 % (1077870)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=3491291711: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)
% 0.21/0.30 % (1077872)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2683444535:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.30 % (1077873)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=1499578928:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.30 % (1077869)Instruction limit reached!
% 0.21/0.30 % (1077869)------------------------------
% 0.21/0.30 % (1077869)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (1077869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (1077869)CaDiCaL version: 2.1.3
% 0.21/0.30 % (1077869)Termination reason: Instruction limit
% 0.21/0.30 % (1077869)Termination phase: Saturation
% 0.21/0.30 % (1077869)Time elapsed: 0.003 s
% 0.21/0.30 % (1077869)Peak memory usage: 12 MB
% 0.21/0.30 % (1077869)Instructions burned: 4 (million)
% 0.21/0.30 % (1077879)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3385125950:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.30 % (1077868)Instruction limit reached!
% 0.21/0.30 % (1077868)------------------------------
% 0.21/0.30 % (1077868)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (1077868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (1077868)CaDiCaL version: 2.1.3
% 0.21/0.30 % (1077868)Termination reason: Instruction limit
% 0.21/0.30 % (1077868)Termination phase: Saturation
% 0.21/0.30 % (1077868)Time elapsed: 0.011 s
% 0.21/0.30 % (1077868)Peak memory usage: 12 MB
% 0.21/0.30 % (1077868)Instructions burned: 20 (million)
% 0.21/0.30 % (1077879)Instruction limit reached!
% 0.21/0.30 % (1077879)------------------------------
% 0.21/0.30 % (1077879)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (1077879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (1077879)CaDiCaL version: 2.1.3
% 0.21/0.30 % (1077879)Termination reason: Instruction limit
% 0.21/0.30 % (1077879)Termination phase: Saturation
% 0.21/0.30 % (1077879)Time elapsed: 0.002 s
% 0.21/0.30 % (1077879)Peak memory usage: 12 MB
% 0.21/0.30 % (1077879)Instructions burned: 5 (million)
% 0.21/0.30 % (1077873) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1077862-1077873"...
% 0.21/0.30 % (1077873)...printing done.
% 0.21/0.30 % (1077873)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% 0.21/0.30 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.21/0.30 thf(type_def_6, type, 'type/nums/num': $tType).
% 0.21/0.30 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.30 thf(func_def_0, type, 'const/trivia/I': !>[X0: $tType]:((X0 > X0))).
% 0.21/0.30 thf(func_def_1, type, 'const/realax/real_of_num': ('type/nums/num' > 'type/realax/real')).
% 0.21/0.30 thf(func_def_2, type, 'const/nums/NUMERAL': ('type/nums/num' > 'type/nums/num')).
% 0.21/0.30 thf(func_def_3, type, 'const/nums/_0': 'type/nums/num').
% 0.21/0.30 thf(func_def_4, type, 'const/iterate/sum': !>[X0: $tType]:(((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real'))).
% 0.21/0.30 thf(func_def_5, type, 'const/iterate/..': ('type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o)).
% 0.21/0.30 thf(func_def_6, type, 'const/arith/<=': ('type/nums/num' > 'type/nums/num' > $o)).
% 0.21/0.30 thf(func_def_7, type, 'const/arith/<': ('type/nums/num' > 'type/nums/num' > $o)).
% 0.21/0.30 thf(func_def_11, type, vNOT: ($o > $o)).
% 0.21/0.30 thf(func_def_12, type, sP0: (('type/nums/num' > 'type/realax/real') > 'type/nums/num' > 'type/nums/num' > $o)).
% 0.21/0.30 thf(func_def_13, type, sK1: (('type/nums/num' > 'type/realax/real') > 'type/nums/num' > 'type/nums/num' > 'type/nums/num')).
% 0.21/0.30 thf(func_def_14, type, sK2: ('type/nums/num' > 'type/realax/real')).
% 0.21/0.30 thf(func_def_15, type, sK3: 'type/nums/num').
% 0.21/0.30 thf(func_def_16, type, sK4: 'type/nums/num').
% 0.21/0.30 thf(func_def_17, type, sF5: $o).
% 0.21/0.30 thf(func_def_18, type, sF6: 'type/nums/num').
% 0.21/0.30 thf(func_def_19, type, sF7: 'type/realax/real').
% 0.21/0.30 thf(func_def_20, type, sF8: 'type/realax/real').
% 0.21/0.30 thf(func_def_22, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.30 thf(func_def_23, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.30 thf(f2,axiom,(
% 0.21/0.30 ! [X1 : 'type/nums/num',X0 : 'type/nums/num'] : (~('const/arith/<' @ X0 @ X1) = (('const/arith/<=' @ X1 @ X0)))),
% 0.21/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/arith/NOT_LT_')).
% 0.21/0.30 thf(f3,axiom,(
% 0.21/0.30 ! [X1 : 'type/nums/num',X2 : 'type/nums/num',X0 : 'type/nums/num'] : ((('const/arith/<=' @ X0 @ X1) & ('const/arith/<=' @ X1 @ X2)) => ('const/arith/<=' @ X0 @ X2))),
% 0.21/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/arith/LE_TRANS_')).
% 0.21/0.30 thf(f4,axiom,(
% 0.21/0.30 ! [X1 : 'type/nums/num',X0 : ('type/nums/num' > 'type/realax/real'),X2 : 'type/nums/num'] : (! [X3 : 'type/nums/num'] : ((('const/arith/<=' @ X1 @ X3) & ('const/arith/<=' @ X3 @ X2)) => (((X0 @ X3)) = (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))) => ((('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)) = (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')))))),
% 0.21/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_EQ_0_NUMSEG_')).
% 0.21/0.30 thf(f5,conjecture,(
% 0.21/0.30 ! [X2 : 'type/nums/num',X1 : 'type/nums/num',X0 : ('type/nums/num' > 'type/realax/real')] : (('const/arith/<' @ X2 @ X1) => ((('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)) = (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')))))),
% 0.21/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_TRIV_NUMSEG_')).
% 0.21/0.30 thf(f6,negated_conjecture,(
% 0.21/0.30 ~ ! [X2 : 'type/nums/num',X1 : 'type/nums/num',X0 : ('type/nums/num' > 'type/realax/real')] : (('const/arith/<' @ X2 @ X1) => ((('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)) = (('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0')))))),
% 0.21/0.30 inference(negated_conjecture,[status(cth)],[f5])).
% 0.21/0.30 thf(f7,plain,(
% 0.21/0.30 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : ((('const/arith/<=' @ X2 @ X0) & ('const/arith/<=' @ X0 @ X1)) => ('const/arith/<=' @ X2 @ X1))),
% 0.21/0.30 inference(rectify,[],[f3])).
% 0.21/0.30 thf(f8,plain,(
% 0.21/0.30 ! [X2 : 'type/nums/num',X1 : 'type/nums/num',X0 : 'type/nums/num'] : ((((('const/arith/<=' @ X0 @ X1)) = $true) & ($true = (('const/arith/<=' @ X2 @ X0)))) => ($true = (('const/arith/<=' @ X2 @ X1))))),
% 0.21/0.30 inference(fool_elimination,[],[f7])).
% 0.21/0.30 thf(f9,plain,(
% 0.21/0.30 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (~('const/arith/<' @ X1 @ X0) = (('const/arith/<=' @ X0 @ X1)))),
% 0.21/0.30 inference(rectify,[],[f2])).
% 0.21/0.30 thf(f10,plain,(
% 0.21/0.30 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ((('const/arith/<=' @ X0 @ X1)) = ((~ ('const/arith/<' @ X1 @ X0))))),
% 0.21/0.30 inference(fool_elimination,[],[f9])).
% 0.21/0.30 thf(f11,plain,(
% 0.21/0.30 ! [X0 : 'type/nums/num',X1 : ('type/nums/num' > 'type/realax/real'),X2 : 'type/nums/num'] : (! [X3 : 'type/nums/num'] : ((('const/arith/<=' @ X0 @ X3) & ('const/arith/<=' @ X3 @ X2)) => ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = ((X1 @ X3)))) => ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X2) @ X1))))),
% 0.21/0.30 inference(rectify,[],[f4])).
% 0.21/0.30 thf(f12,plain,(
% 0.21/0.30 ! [X1 : ('type/nums/num' > 'type/realax/real'),X0 : 'type/nums/num',X2 : 'type/nums/num'] : (! [X3 : 'type/nums/num'] : ((((('const/arith/<=' @ X3 @ X2)) = $true) & ($true = (('const/arith/<=' @ X0 @ X3)))) => ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = ((X1 @ X3)))) => ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X2) @ X1))))),
% 0.21/0.30 inference(fool_elimination,[],[f11])).
% 0.21/0.30 thf(f13,plain,(
% 0.21/0.30 ~ ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : ('type/nums/num' > 'type/realax/real')] : (('const/arith/<' @ X0 @ X1) => ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X0) @ X2))))),
% 0.21/0.30 inference(rectify,[],[f6])).
% 0.21/0.30 thf(f14,plain,(
% 0.21/0.30 ~ ! [X1 : 'type/nums/num',X0 : 'type/nums/num',X2 : ('type/nums/num' > 'type/realax/real')] : (((('const/arith/<' @ X0 @ X1)) = $true) => ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X0) @ X2))))),
% 0.21/0.30 inference(fool_elimination,[],[f13])).
% 0.21/0.30 thf(f15,plain,(
% 0.21/0.30 ? [X2 : ('type/nums/num' > 'type/realax/real'),X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/arith/<' @ X0 @ X1)) = $true) & ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X0) @ X2))))),
% 0.21/0.30 inference(ennf_transformation,[],[f14])).
% 0.21/0.30 thf(f16,plain,(
% 0.21/0.30 ! [X2 : 'type/nums/num',X1 : 'type/nums/num',X0 : 'type/nums/num'] : (($true = (('const/arith/<=' @ X2 @ X1))) | (((('const/arith/<=' @ X0 @ X1)) != $true) | ($true != (('const/arith/<=' @ X2 @ X0)))))),
% 0.21/0.30 inference(ennf_transformation,[],[f8])).
% 0.21/0.30 thf(f17,plain,(
% 0.21/0.30 ! [X1 : 'type/nums/num',X2 : 'type/nums/num',X0 : 'type/nums/num'] : (($true = (('const/arith/<=' @ X2 @ X1))) | ($true != (('const/arith/<=' @ X2 @ X0))) | ((('const/arith/<=' @ X0 @ X1)) != $true))),
% 0.21/0.30 inference(flattening,[],[f16])).
% 0.21/0.30 thf(f18,plain,(
% 0.21/0.30 ! [X1 : ('type/nums/num' > 'type/realax/real'),X0 : 'type/nums/num',X2 : 'type/nums/num'] : (((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X2) @ X1))) | ? [X3 : 'type/nums/num'] : (((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != ((X1 @ X3))) & (((('const/arith/<=' @ X3 @ X2)) = $true) & ($true = (('const/arith/<=' @ X0 @ X3))))))),
% 0.21/0.30 inference(ennf_transformation,[],[f12])).
% 0.21/0.30 thf(f19,plain,(
% 0.21/0.30 ! [X1 : ('type/nums/num' > 'type/realax/real'),X0 : 'type/nums/num',X2 : 'type/nums/num'] : (? [X3 : 'type/nums/num'] : (($true = (('const/arith/<=' @ X0 @ X3))) & ((('const/arith/<=' @ X3 @ X2)) = $true) & ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != ((X1 @ X3)))) | ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X2) @ X1))))),
% 0.21/0.30 inference(flattening,[],[f18])).
% 0.21/0.30 thf(f20,definition,(
% 0.21/0.30 ! [X0 : 'type/nums/num',X2 : 'type/nums/num',X1 : ('type/nums/num' > 'type/realax/real')] : (? [X3 : 'type/nums/num'] : (($true = (('const/arith/<=' @ X0 @ X3))) & ((('const/arith/<=' @ X3 @ X2)) = $true) & ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != ((X1 @ X3)))) | ~ ($true = ((sP0 @ X1 @ X2 @ X0))))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.21/0.30 thf(f21,plain,(
% 0.21/0.30 ! [X1 : ('type/nums/num' > 'type/realax/real'),X0 : 'type/nums/num',X2 : 'type/nums/num'] : (($true = ((sP0 @ X1 @ X2 @ X0))) | ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X2) @ X1))))),
% 0.21/0.30 inference(definition_folding,[],[f19,f20])).
% 0.21/0.30 thf(f22,plain,(
% 0.21/0.30 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : (((('const/arith/<=' @ X1 @ X0)) = $true) | ((('const/arith/<=' @ X1 @ X2)) != $true) | ($true != (('const/arith/<=' @ X2 @ X0))))),
% 0.21/0.30 inference(rectify,[],[f17])).
% 0.21/0.30 thf(f23,plain,(
% 0.21/0.30 ! [X0 : 'type/nums/num',X2 : 'type/nums/num',X1 : ('type/nums/num' > 'type/realax/real')] : (? [X3 : 'type/nums/num'] : (($true = (('const/arith/<=' @ X0 @ X3))) & ((('const/arith/<=' @ X3 @ X2)) = $true) & ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != ((X1 @ X3)))) | ($true != ((sP0 @ X1 @ X2 @ X0))))),
% 0.21/0.30 inference(nnf_transformation,[],[f20])).
% 0.21/0.30 thf(f24,plain,(
% 0.21/0.30 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : ('type/nums/num' > 'type/realax/real')] : (? [X3 : 'type/nums/num'] : (($true = (('const/arith/<=' @ X0 @ X3))) & ($true = (('const/arith/<=' @ X3 @ X1))) & ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != ((X2 @ X3)))) | ($true != ((sP0 @ X2 @ X1 @ X0))))),
% 0.21/0.30 inference(rectify,[],[f23])).
% 0.21/0.30 thf(f25,plain,(
% 0.21/0.30 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : ('type/nums/num' > 'type/realax/real')] : ((($true = (('const/arith/<=' @ X0 @ (sK1 @ X2 @ X1 @ X0)))) & ($true = (('const/arith/<=' @ (sK1 @ X2 @ X1 @ X0) @ X1))) & ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != ((X2 @ (sK1 @ X2 @ X1 @ X0))))) | ($true != ((sP0 @ X2 @ X1 @ X0))))),
% 0.21/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,sK1 @ X2 @ X1 @ X0)],[f24])).
% 0.21/0.30 thf(f26,plain,(
% 0.21/0.30 ! [X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num',X2 : 'type/nums/num'] : (($true = ((sP0 @ X0 @ X2 @ X1))) | ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0))))),
% 0.21/0.30 inference(rectify,[],[f21])).
% 0.21/0.30 thf(f27,plain,(
% 0.21/0.30 ? [X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num',X2 : 'type/nums/num'] : (($true = (('const/arith/<' @ X1 @ X2))) & ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X2 @ X1) @ X0))))),
% 0.21/0.30 inference(rectify,[],[f15])).
% 0.21/0.30 thf(f28,plain,(
% 0.21/0.30 ((('const/arith/<' @ sK3 @ sK4)) = $true) & ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK4 @ sK3) @ sK2)))),
% 0.21/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f27])).
% 0.21/0.30 thf(f29,plain,(
% 0.21/0.30 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/arith/<=' @ X0 @ X1)) = ((~ ('const/arith/<' @ X1 @ X0))))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f10])).
% 0.21/0.30 thf(f30,plain,(
% 0.21/0.30 ( ! [X2 : 'type/nums/num',X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/arith/<=' @ X1 @ X0)) = $true) | ((('const/arith/<=' @ X1 @ X2)) != $true) | ($true != (('const/arith/<=' @ X2 @ X0)))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f22])).
% 0.21/0.30 thf(f33,plain,(
% 0.21/0.30 ( ! [X2 : ('type/nums/num' > 'type/realax/real'),X0 : 'type/nums/num',X1 : 'type/nums/num'] : (($true = (('const/arith/<=' @ (sK1 @ X2 @ X1 @ X0) @ X1))) | ($true != ((sP0 @ X2 @ X1 @ X0)))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f25])).
% 0.21/0.30 thf(f34,plain,(
% 0.21/0.30 ( ! [X2 : ('type/nums/num' > 'type/realax/real'),X0 : 'type/nums/num',X1 : 'type/nums/num'] : (($true = (('const/arith/<=' @ X0 @ (sK1 @ X2 @ X1 @ X0)))) | ($true != ((sP0 @ X2 @ X1 @ X0)))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f25])).
% 0.21/0.30 thf(f35,plain,(
% 0.21/0.30 ( ! [X2 : 'type/nums/num',X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num'] : (((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0))) | ($true = ((sP0 @ X0 @ X2 @ X1)))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f26])).
% 0.21/0.30 thf(f36,plain,(
% 0.21/0.30 ((('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) != (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK4 @ sK3) @ sK2)))),
% 0.21/0.30 inference(cnf_transformation,[],[f28])).
% 0.21/0.30 thf(f37,plain,(
% 0.21/0.30 ((('const/arith/<' @ sK3 @ sK4)) = $true)),
% 0.21/0.30 inference(cnf_transformation,[],[f28])).
% 0.21/0.30 thf(f40,definition,(
% 0.21/0.30 (sF5 = (('const/arith/<' @ sK3 @ sK4)))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[sF5])],[function_definition])).
% 0.21/0.30 thf(f41,plain,(
% 0.21/0.30 ((('const/arith/<' @ sK3 @ sK4)) = sF5)),
% 0.21/0.30 inference(reorient_equations,[],[f40])).
% 0.21/0.30 thf(f42,plain,(
% 0.21/0.30 ($true = sF5)),
% 0.21/0.30 inference(definition_folding,[],[f37,f41])).
% 0.21/0.30 thf(f43,definition,(
% 0.21/0.30 (sF6 = (('const/nums/NUMERAL' @ 'const/nums/_0')))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[sF6])],[function_definition])).
% 0.21/0.30 thf(f44,plain,(
% 0.21/0.30 ((('const/nums/NUMERAL' @ 'const/nums/_0')) = sF6)),
% 0.21/0.30 inference(reorient_equations,[],[f43])).
% 0.21/0.30 thf(f45,definition,(
% 0.21/0.30 (sF7 = (('const/realax/real_of_num' @ sF6)))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[sF7])],[function_definition])).
% 0.21/0.30 thf(f46,plain,(
% 0.21/0.30 ((('const/realax/real_of_num' @ sF6)) = sF7)),
% 0.21/0.30 inference(reorient_equations,[],[f45])).
% 0.21/0.30 thf(f47,definition,(
% 0.21/0.30 (sF8 = (('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK4 @ sK3) @ sK2)))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[sF8])],[function_definition])).
% 0.21/0.30 thf(f48,plain,(
% 0.21/0.30 (sF8 != sF7)),
% 0.21/0.30 inference(definition_folding,[],[f36,f47,f46,f44])).
% 0.21/0.30 thf(f50,plain,(
% 0.21/0.30 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/arith/<=' @ X0 @ X1)) = $false) | ($true = ((~ ('const/arith/<' @ X1 @ X0))))) )),
% 0.21/0.30 inference(iff_proxy_clausification,[],[f29])).
% 0.21/0.30 thf(f51,plain,(
% 0.21/0.30 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/arith/<' @ X1 @ X0)) = $false) | ((('const/arith/<=' @ X0 @ X1)) = $false)) )),
% 0.21/0.30 inference(not_proxy_clausification,[],[f50])).
% 0.21/0.30 thf(f53,plain,(
% 0.21/0.30 (sF5 = $false) | ((('const/arith/<' @ sK3 @ sK4)) = $true)),
% 0.21/0.30 inference(iff_proxy_clausification,[],[f41])).
% 0.21/0.30 thf(f56,definition,(
% 0.21/0.30 spl9_1 <=> ($true = sF5)),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition])).
% 0.21/0.30 thf(f58,plain,(
% 0.21/0.30 ($true = sF5) | ~spl9_1),
% 0.21/0.30 inference(avatar_component_clause,[],[f56])).
% 0.21/0.30 thf(f60,definition,(
% 0.21/0.30 spl9_2 <=> ((('const/arith/<' @ sK3 @ sK4)) = $false)),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition])).
% 0.21/0.30 thf(f61,plain,(
% 0.21/0.30 ((('const/arith/<' @ sK3 @ sK4)) != $false) | spl9_2),
% 0.21/0.30 inference(avatar_component_clause,[],[f60])).
% 0.21/0.30 thf(f62,plain,(
% 0.21/0.30 ((('const/arith/<' @ sK3 @ sK4)) = $false) | ~spl9_2),
% 0.21/0.30 inference(avatar_component_clause,[],[f60])).
% 0.21/0.30 thf(f65,definition,(
% 0.21/0.30 spl9_3 <=> (sF5 = $false)),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition])).
% 0.21/0.30 thf(f67,plain,(
% 0.21/0.30 (sF5 = $false) | ~spl9_3),
% 0.21/0.30 inference(avatar_component_clause,[],[f65])).
% 0.21/0.30 thf(f69,definition,(
% 0.21/0.30 spl9_4 <=> ((('const/arith/<' @ sK3 @ sK4)) = $true)),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition])).
% 0.21/0.30 thf(f71,plain,(
% 0.21/0.30 ((('const/arith/<' @ sK3 @ sK4)) = $true) | ~spl9_4),
% 0.21/0.30 inference(avatar_component_clause,[],[f69])).
% 0.21/0.30 thf(f72,plain,(
% 0.21/0.30 spl9_3 | spl9_4),
% 0.21/0.30 inference(avatar_split_clause,[],[f53,f69,f65])).
% 0.21/0.30 thf(f73,plain,(
% 0.21/0.30 spl9_1),
% 0.21/0.30 inference(avatar_split_clause,[],[f42,f56])).
% 0.21/0.30 thf(f74,plain,(
% 0.21/0.30 ($true = $false) | (~spl9_1 | ~spl9_3)),
% 0.21/0.30 inference(forward_demodulation,[],[f67,f58])).
% 0.21/0.30 thf(f75,plain,(
% 0.21/0.30 $false | (~spl9_1 | ~spl9_3)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f74])).
% 0.21/0.30 thf(f76,plain,(
% 0.21/0.30 ~spl9_1 | ~spl9_3),
% 0.21/0.30 inference(avatar_contradiction_clause,[],[f75])).
% 0.21/0.30 thf(f90,plain,(
% 0.21/0.30 ($true = $false) | (~spl9_2 | ~spl9_4)),
% 0.21/0.30 inference(forward_demodulation,[],[f71,f62])).
% 0.21/0.30 thf(f91,plain,(
% 0.21/0.30 $false | (~spl9_2 | ~spl9_4)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f90])).
% 0.21/0.30 thf(f92,plain,(
% 0.21/0.30 ~spl9_2 | ~spl9_4),
% 0.21/0.30 inference(avatar_contradiction_clause,[],[f91])).
% 0.21/0.30 thf(f101,plain,(
% 0.21/0.30 ($false != $false) | ((('const/arith/<=' @ sK4 @ sK3)) = $false) | spl9_2),
% 0.21/0.30 inference(constrained_superposition,[],[f61,f51])).
% 0.21/0.30 thf(f102,plain,(
% 0.21/0.30 ((('const/arith/<=' @ sK4 @ sK3)) = $false) | spl9_2),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f101])).
% 0.21/0.30 thf(f109,plain,(
% 0.21/0.30 ( ! [X0 : 'type/nums/num'] : (($true = $false) | ((('const/arith/<=' @ sK4 @ X0)) != $true) | ($true != (('const/arith/<=' @ X0 @ sK3)))) ) | spl9_2),
% 0.21/0.30 inference(constrained_superposition,[],[f102,f30])).
% 0.21/0.30 thf(f110,plain,(
% 0.21/0.30 ( ! [X0 : 'type/nums/num'] : (($true != (('const/arith/<=' @ X0 @ sK3))) | ((('const/arith/<=' @ sK4 @ X0)) != $true)) ) | spl9_2),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f109])).
% 0.21/0.30 thf(f149,plain,(
% 0.21/0.30 ( ! [X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num'] : (($true != (('const/arith/<=' @ sK4 @ (sK1 @ X0 @ sK3 @ X1)))) | ($true != ((sP0 @ X0 @ sK3 @ X1))) | ($true != $true)) ) | spl9_2),
% 0.21/0.30 inference(constrained_superposition,[],[f110,f33])).
% 0.21/0.30 thf(f153,plain,(
% 0.21/0.30 ( ! [X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num'] : (($true != (('const/arith/<=' @ sK4 @ (sK1 @ X0 @ sK3 @ X1)))) | ($true != ((sP0 @ X0 @ sK3 @ X1)))) ) | spl9_2),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f149])).
% 0.21/0.30 thf(f181,plain,(
% 0.21/0.30 ( ! [X0 : ('type/nums/num' > 'type/realax/real')] : ((((sP0 @ X0 @ sK3 @ sK4)) != $true) | ($true != $true) | (((sP0 @ X0 @ sK3 @ sK4)) != $true)) ) | spl9_2),
% 0.21/0.30 inference(constrained_superposition,[],[f153,f34])).
% 0.21/0.30 thf(f185,plain,(
% 0.21/0.30 ( ! [X0 : ('type/nums/num' > 'type/realax/real')] : ((((sP0 @ X0 @ sK3 @ sK4)) != $true) | ($true != $true)) ) | spl9_2),
% 0.21/0.30 inference(duplicate_literal_removal,[],[f181])).
% 0.21/0.30 thf(f186,plain,(
% 0.21/0.30 ( ! [X0 : ('type/nums/num' > 'type/realax/real')] : ((((sP0 @ X0 @ sK3 @ sK4)) != $true)) ) | spl9_2),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f185])).
% 0.21/0.30 thf(f231,plain,(
% 0.21/0.30 ( ! [X2 : 'type/nums/num',X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num'] : (($true = ((sP0 @ X0 @ X2 @ X1))) | ((('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)) = (('const/realax/real_of_num' @ sF6)))) )),
% 0.21/0.30 inference(forward_demodulation,[],[f35,f44])).
% 0.21/0.30 thf(f232,plain,(
% 0.21/0.30 ( ! [X2 : 'type/nums/num',X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num'] : (((('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)) = sF7) | ($true = ((sP0 @ X0 @ X2 @ X1)))) )),
% 0.21/0.30 inference(forward_demodulation,[],[f231,f46])).
% 0.21/0.30 thf(f234,plain,(
% 0.21/0.30 (sF8 = sF7) | ($true = ((sP0 @ sK2 @ sK3 @ sK4)))),
% 0.21/0.30 inference(constrained_superposition,[],[f47,f232])).
% 0.21/0.30 thf(f236,plain,(
% 0.21/0.30 ($true = ((sP0 @ sK2 @ sK3 @ sK4)))),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f234,f48])).
% 0.21/0.30 thf(f239,plain,(
% 0.21/0.30 $false | spl9_2),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f236,f186])).
% 0.21/0.30 thf(f240,plain,(
% 0.21/0.30 spl9_2),
% 0.21/0.30 inference(avatar_contradiction_clause,[],[f239])).
% 0.21/0.30 cnf(s2, plain, spl9_3 | spl9_4, inference(sat_conversion,[],[f72])).
% 0.21/0.30 cnf(s3, plain, spl9_1, inference(sat_conversion,[],[f73])).
% 0.21/0.30 cnf(s4, plain, ~spl9_1 | ~spl9_3, inference(sat_conversion,[],[f76])).
% 0.21/0.30 cnf(s5, plain, ~spl9_2 | ~spl9_4, inference(sat_conversion,[],[f92])).
% 0.21/0.30 cnf(s7, plain, spl9_2, inference(sat_conversion,[],[f240])).
% 0.21/0.30 cnf(s8, plain, ~spl9_4, inference(rat,[],[s5,s7])).
% 0.21/0.30 cnf(s9, plain, ~spl9_3, inference(rat,[],[s4,s3])).
% 0.21/0.30 cnf(s10, plain, $false, inference(rat,[],[s2,s8,s9])).
% 0.21/0.30 thf(f241,plain,(
% 0.21/0.30 $false),
% 0.21/0.30 inference(avatar_sat_refutation,[],[s10])).
% 0.21/0.30 % SZS output end Proof for theBenchmark
% 0.21/0.30 % (1077873)------------------------------
% 0.21/0.30 % (1077873)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (1077873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (1077873)CaDiCaL version: 2.1.3
% 0.21/0.30 % (1077873)Termination reason: Refutation
% 0.21/0.30 % (1077873)Time elapsed: 0.013 s
% 0.21/0.30 % (1077873)Peak memory usage: 13 MB
% 0.21/0.30 % (1077873)Instructions burned: 22 (million)
% 0.21/0.30 % (1077862)Success in time 0.045 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------