%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA107^1 : 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 : n018.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 07:45:55 AM UTC 2026
% Result : Theorem 0.23s 0.31s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA107^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 % Computer : n018.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 17:44:11 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.25 Running higher-order theorem proving
% 0.23/0.26 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
% 0.23/0.31 % (406969)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.31 % (406978)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=483255211:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.31 % (406978)Refutation not found, incomplete strategy
% 0.23/0.31 % (406978)------------------------------
% 0.23/0.31 % (406978)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (406978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (406978)CaDiCaL version: 2.1.3
% 0.23/0.31 % (406978)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.31 % (406978)Time elapsed: 0.001 s
% 0.23/0.31 % (406978)Peak memory usage: 12 MB
% 0.23/0.31 % (406978)Instructions burned: 1 (million)
% 0.23/0.31 % (406978)------------------------------
% 0.23/0.31 % (406978)------------------------------
% 0.23/0.31 % (406974)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=104204052:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.31 % (406975)lrs+10_16_si=on:nwc=1.5:random_seed=1403897010:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.31 % (406976)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1219603134:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.31 % (406977)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=1615337651:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.23/0.31 % (406976)Refutation not found, incomplete strategy
% 0.23/0.31 % (406976)------------------------------
% 0.23/0.31 % (406976)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (406974)Refutation not found, incomplete strategy
% 0.23/0.31 % (406974)------------------------------
% 0.23/0.31 % (406974)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (406976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (406974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (406976)CaDiCaL version: 2.1.3
% 0.23/0.31 % (406974)CaDiCaL version: 2.1.3
% 0.23/0.31 % (406974)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.31 % (406974)Time elapsed: 0.002 s
% 0.23/0.31 % (406976)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.31 % (406976)Time elapsed: 0.002 s
% 0.23/0.31 % (406974)Peak memory usage: 12 MB
% 0.23/0.31 % (406976)Peak memory usage: 12 MB
% 0.23/0.31 % (406976)Instructions burned: 2 (million)
% 0.23/0.31 % (406974)Instructions burned: 2 (million)
% 0.23/0.31 % (406977)Refutation not found, incomplete strategy
% 0.23/0.31 % (406977)------------------------------
% 0.23/0.31 % (406977)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (406977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (406977)CaDiCaL version: 2.1.3
% 0.23/0.31 % (406977)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.31 % (406977)Time elapsed: 0.002 s
% 0.23/0.31 % (406977)Peak memory usage: 12 MB
% 0.23/0.31 % (406977)Instructions burned: 2 (million)
% 0.23/0.31 % (406979)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3401130929:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.31 % (406976)------------------------------
% 0.23/0.31 % (406976)------------------------------
% 0.23/0.31 % (406974)------------------------------
% 0.23/0.31 % (406974)------------------------------
% 0.23/0.31 % (406977)------------------------------
% 0.23/0.31 % (406977)------------------------------
% 0.23/0.31 % (406975) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-406969-406975"...
% 0.23/0.31 % (406979) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-406969-406979"...
% 0.23/0.31 % (406979)...printing done.
% 0.23/0.31 % (406979)Refutation found. Thanks to Tanya!
% 0.23/0.31 % SZS status Theorem for theBenchmark
% 0.23/0.31 % SZS output start Proof for theBenchmark
% 0.23/0.31 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.23/0.31 thf(type_def_6, type, 'type/nums/num': $tType).
% 0.23/0.31 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.31 thf(func_def_0, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.23/0.31 thf(func_def_1, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.23/0.31 thf(func_def_2, type, 'const/realax/real_abs': ('type/realax/real' > 'type/realax/real')).
% 0.23/0.31 thf(func_def_3, type, 'const/iterate/sum': !>[X0: $tType]:(((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real'))).
% 0.23/0.31 thf(func_def_4, type, 'const/iterate/..': ('type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o)).
% 0.23/0.31 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.23/0.31 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.23/0.31 thf(func_def_10, type, sK0: ('type/nums/num' > 'type/realax/real')).
% 0.23/0.31 thf(func_def_11, type, sK1: 'type/nums/num').
% 0.23/0.31 thf(func_def_12, type, sK2: 'type/nums/num').
% 0.23/0.31 thf(f1,axiom,(
% 0.23/0.31 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > $o)] : (('const/sets/FINITE' @ X0 @ X2) => ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/iterate/sum' @ X0 @ X2 @ X1)) @ ('const/iterate/sum' @ X0 @ X2 @ (^[X3 : X0] : (('const/realax/real_abs' @ (X1 @ X3)))))))),
% 0.23/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_ABS_')).
% 0.23/0.31 thf(f2,axiom,(
% 0.23/0.31 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1))),
% 0.23/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/FINITE_NUMSEG_')).
% 0.23/0.31 thf(f3,conjecture,(
% 0.23/0.31 ! [X1 : 'type/nums/num',X0 : ('type/nums/num' > 'type/realax/real'),X2 : 'type/nums/num'] : ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ (^[X3 : 'type/nums/num'] : (('const/realax/real_abs' @ (X0 @ X3))))))),
% 0.23/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_ABS_NUMSEG_')).
% 0.23/0.31 thf(f4,negated_conjecture,(
% 0.23/0.31 ~ ! [X1 : 'type/nums/num',X0 : ('type/nums/num' > 'type/realax/real'),X2 : 'type/nums/num'] : ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ (^[X3 : 'type/nums/num'] : (('const/realax/real_abs' @ (X0 @ X3))))))),
% 0.23/0.31 inference(negated_conjecture,[status(cth)],[f3])).
% 0.23/0.31 thf(f5,plain,(
% 0.23/0.31 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > $o)] : (('const/sets/FINITE' @ X0 @ X2) => ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/iterate/sum' @ X0 @ X2 @ X1)) @ ('const/iterate/sum' @ X0 @ X2 @ (^[X3 : X0] : (('const/realax/real_abs' @ (X1 @ X3)))))))),
% 0.23/0.31 inference(rectify,[],[f1])).
% 0.23/0.31 thf(f6,plain,(
% 0.23/0.31 ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > 'type/realax/real')] : (((('const/sets/FINITE' @ X0 @ X2)) = $true) => ($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/iterate/sum' @ X0 @ X2 @ X1)) @ ('const/iterate/sum' @ X0 @ X2 @ (^[Y0 : X0]: ('const/realax/real_abs' @ (X1 @ Y0))))))))),
% 0.23/0.31 inference(fool_elimination,[],[f5])).
% 0.23/0.31 thf(f7,plain,(
% 0.23/0.31 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1))),
% 0.23/0.31 inference(rectify,[],[f2])).
% 0.23/0.31 thf(f8,plain,(
% 0.23/0.31 ! [X1 : 'type/nums/num',X0 : 'type/nums/num'] : ((('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1))) = $true)),
% 0.23/0.31 inference(fool_elimination,[],[f7])).
% 0.23/0.31 thf(f9,plain,(
% 0.23/0.31 ~ ! [X0 : 'type/nums/num',X1 : ('type/nums/num' > 'type/realax/real'),X2 : 'type/nums/num'] : ('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X2) @ X1)) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X2) @ (^[X3 : 'type/nums/num'] : (('const/realax/real_abs' @ (X1 @ X3))))))),
% 0.23/0.31 inference(rectify,[],[f4])).
% 0.23/0.31 thf(f10,plain,(
% 0.23/0.31 ~ ! [X0 : 'type/nums/num',X1 : ('type/nums/num' > 'type/realax/real'),X2 : 'type/nums/num'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X2) @ X1)) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X2) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_abs' @ (X1 @ Y0)))))) = $true)),
% 0.23/0.31 inference(fool_elimination,[],[f9])).
% 0.23/0.31 thf(f11,plain,(
% 0.23/0.31 ? [X1 : ('type/nums/num' > 'type/realax/real'),X2 : 'type/nums/num',X0 : 'type/nums/num'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X2) @ X1)) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X2) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_abs' @ (X1 @ Y0)))))) != $true)),
% 0.23/0.31 inference(ennf_transformation,[],[f10])).
% 0.23/0.31 thf(f12,plain,(
% 0.23/0.31 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > $o)] : (($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/iterate/sum' @ X0 @ X2 @ X1)) @ ('const/iterate/sum' @ X0 @ X2 @ (^[Y0 : X0]: ('const/realax/real_abs' @ (X1 @ Y0))))))) | ((('const/sets/FINITE' @ X0 @ X2)) != $true))),
% 0.23/0.31 inference(ennf_transformation,[],[f6])).
% 0.23/0.31 thf(f13,plain,(
% 0.23/0.31 ? [X0 : ('type/nums/num' > 'type/realax/real'),X1 : 'type/nums/num',X2 : 'type/nums/num'] : ((('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X2 @ X1) @ X0)) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X2 @ X1) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_abs' @ (X0 @ Y0)))))) != $true)),
% 0.23/0.31 inference(rectify,[],[f11])).
% 0.23/0.31 thf(f14,plain,(
% 0.23/0.31 ((('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK2 @ sK1) @ sK0)) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK2 @ sK1) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_abs' @ (sK0 @ Y0)))))) != $true)),
% 0.23/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f13])).
% 0.23/0.31 thf(f15,plain,(
% 0.23/0.31 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ((('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X0))) = $true)),
% 0.23/0.31 inference(rectify,[],[f8])).
% 0.23/0.31 thf(f16,plain,(
% 0.23/0.31 ((('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK2 @ sK1) @ sK0)) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK2 @ sK1) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_abs' @ (sK0 @ Y0)))))) != $true)),
% 0.23/0.31 inference(cnf_transformation,[],[f14])).
% 0.23/0.31 thf(f17,plain,(
% 0.23/0.31 ( ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X0))) = $true)) )),
% 0.23/0.31 inference(cnf_transformation,[],[f15])).
% 0.23/0.31 thf(f18,plain,(
% 0.23/0.31 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > 'type/realax/real')] : (((('const/sets/FINITE' @ X0 @ X2)) != $true) | ($true = (('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/iterate/sum' @ X0 @ X2 @ X1)) @ ('const/iterate/sum' @ X0 @ X2 @ (^[Y0 : X0]: ('const/realax/real_abs' @ (X1 @ Y0)))))))) )),
% 0.23/0.31 inference(cnf_transformation,[],[f12])).
% 0.23/0.31 thf(f20,definition,(
% 0.23/0.31 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.23/0.31 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.23/0.31 thf(f23,plain,(
% 0.23/0.31 ($false = (('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK2 @ sK1) @ sK0)) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK2 @ sK1) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_abs' @ (sK0 @ Y0))))))) | ($true != $true)),
% 0.23/0.31 inference(constrained_superposition,[],[f16,f20])).
% 0.23/0.31 thf(f25,plain,(
% 0.23/0.31 ($false = (('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK2 @ sK1) @ sK0)) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ sK2 @ sK1) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_abs' @ (sK0 @ Y0)))))))),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f23])).
% 0.23/0.31 thf(f34,plain,(
% 0.23/0.31 ( ! [X2 : ('type/nums/num' > 'type/realax/real'),X0 : 'type/nums/num',X1 : 'type/nums/num'] : (($true != $true) | ((('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2)) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_abs' @ (X2 @ Y0)))))) = $true)) )),
% 0.23/0.31 inference(constrained_superposition,[],[f18,f17])).
% 0.23/0.31 thf(f36,plain,(
% 0.23/0.31 ( ! [X2 : ('type/nums/num' > 'type/realax/real'),X0 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/realax/real_le' @ ('const/realax/real_abs' @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ X2)) @ ('const/iterate/sum' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1) @ (^[Y0 : 'type/nums/num']: ('const/realax/real_abs' @ (X2 @ Y0)))))) = $true)) )),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f34])).
% 0.23/0.31 thf(f37,plain,(
% 0.23/0.31 ($false = $true)),
% 0.23/0.31 inference(backward_demodulation,[],[f25,f36])).
% 0.23/0.31 thf(f38,plain,(
% 0.23/0.31 $false),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f37])).
% 0.23/0.31 % SZS output end Proof for theBenchmark
% 0.23/0.31 % (406979)------------------------------
% 0.23/0.31 % (406979)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (406979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (406979)CaDiCaL version: 2.1.3
% 0.23/0.31 % (406979)Termination reason: Refutation
% 0.23/0.31 % (406979)Time elapsed: 0.002 s
% 0.23/0.31 % (406979)Peak memory usage: 12 MB
% 0.23/0.31 % (406979)Instructions burned: 5 (million)
% 0.23/0.31 % (406969)Success in time 0.035 s
% 0.23/0.31 % Vampire exiting
%------------------------------------------------------------------------------