%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO531^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 08:48:21 AM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO531^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n015.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 17:16:33 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.21 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
% 0.09/0.26 % (3832920)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.26 % (3832925)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1800068673:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.09/0.26 % (3832925)Refutation not found, incomplete strategy
% 0.09/0.26 % (3832925)------------------------------
% 0.09/0.26 % (3832925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (3832925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (3832925)CaDiCaL version: 2.1.3
% 0.09/0.26 % (3832925)Termination reason: Refutation not found, incomplete strategy
% 0.09/0.26 % (3832925)Time elapsed: 0.002 s
% 0.09/0.26 % (3832925)Peak memory usage: 12 MB
% 0.09/0.26 % (3832925)Instructions burned: 5 (million)
% 0.09/0.26 % (3832925)------------------------------
% 0.09/0.26 % (3832925)------------------------------
% 0.09/0.26 % (3832926)lrs+10_16_si=on:nwc=1.5:random_seed=416637596:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.09/0.26 % (3832928)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=458211378: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)
% 0.09/0.26 % (3832931)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.09/0.26 % (3832931)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
% 0.09/0.26 % (3832928) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3832920-3832928"...
% 0.09/0.26 % (3832933)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=862174704:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.09/0.26 % (3832928)...printing done.
% 0.09/0.26 % (3832931)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=1104971041:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.09/0.26 % (3832933)Instruction limit reached!
% 0.09/0.26 % (3832933)------------------------------
% 0.09/0.26 % (3832933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (3832933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (3832933)CaDiCaL version: 2.1.3
% 0.09/0.26 % (3832933)Termination reason: Instruction limit
% 0.09/0.26 % (3832933)Termination phase: Saturation
% 0.09/0.26 % (3832933)Time elapsed: 0.002 s
% 0.09/0.26 % (3832933)Peak memory usage: 12 MB
% 0.09/0.26 % (3832933)Instructions burned: 6 (million)
% 0.09/0.26 % (3832928)Refutation found. Thanks to Tanya!
% 0.09/0.26 % SZS status Theorem for theBenchmark
% 0.09/0.26 % SZS output start Proof for theBenchmark
% 0.09/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.26 thf(func_def_0, type, eps: (($i > $o) > $i)).
% 0.09/0.26 thf(func_def_2, type, epsa: (($i > $i > $o) > $i)).
% 0.09/0.26 thf(func_def_5, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.09/0.26 thf(func_def_6, type, db2: !>[X0: $tType]:(X0)).
% 0.09/0.26 thf(func_def_7, type, db1: !>[X0: $tType]:(X0)).
% 0.09/0.26 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.09/0.26 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.09/0.26 thf(func_def_10, type, sK0: ((($i > $i > $o) > $i) > $i > $i > $o)).
% 0.09/0.26 thf(func_def_11, type, sK1: ((($i > $i > $o) > $i) > $i)).
% 0.09/0.26 thf(func_def_12, type, sK2: ((($i > $i > $o) > $i) > $i)).
% 0.09/0.26 thf(func_def_13, type, vNOT: ($o > $o)).
% 0.09/0.26 thf(func_def_15, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.09/0.26 thf(func_def_16, type, sK4: (($i > $i > $o) > $i)).
% 0.09/0.26 thf(func_def_17, type, sK5: (($i > $i > $o) > $i)).
% 0.09/0.26 thf(f1,axiom,(
% 0.09/0.26 ! [X0 : ($i > $o)] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps @ X0)))),
% 0.09/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',choiceax)).
% 0.09/0.26 thf(f2,axiom,(
% 0.09/0.26 ((^[X0 : ($i > $i > $o)] : ((eps @ (^[X1 : $i] : (? [X2 : $i] : (X0 @ X1 @ X2)))))) = epsa)),
% 0.09/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',epsad)).
% 0.09/0.26 thf(f3,conjecture,(
% 0.09/0.26 ? [X0 : (($i > $i > $o) > $i)] : ! [X1 : ($i > $i > $o)] : (? [X3 : $i,X2 : $i] : (X1 @ X2 @ X3) => (X1 @ (epsa @ X1) @ (X0 @ X1)))),
% 0.09/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.09/0.26 thf(f4,negated_conjecture,(
% 0.09/0.26 ~ ? [X0 : (($i > $i > $o) > $i)] : ! [X1 : ($i > $i > $o)] : (? [X3 : $i,X2 : $i] : (X1 @ X2 @ X3) => (X1 @ (epsa @ X1) @ (X0 @ X1)))),
% 0.09/0.26 inference(negated_conjecture,[status(cth)],[f3])).
% 0.09/0.26 thf(f5,plain,(
% 0.09/0.26 ! [X0 : ($i > $o)] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps @ X0)))),
% 0.09/0.26 inference(rectify,[],[f1])).
% 0.09/0.26 thf(f6,plain,(
% 0.09/0.26 ! [X0 : ($i > $o)] : (? [X1 : $i] : (((X0 @ X1)) = $true) => (((X0 @ (eps @ X0))) = $true))),
% 0.09/0.26 inference(fool_elimination,[],[f5])).
% 0.09/0.26 thf(f7,plain,(
% 0.09/0.26 ((^[X0 : ($i > $i > $o)] : ((eps @ (^[X1 : $i] : (? [X2 : $i] : (X0 @ X1 @ X2)))))) = epsa)),
% 0.09/0.26 inference(rectify,[],[f2])).
% 0.09/0.26 thf(f8,plain,(
% 0.09/0.26 (epsa = (^[Y0 : $i > $i > $o]: (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.09/0.26 inference(fool_elimination,[],[f7])).
% 0.09/0.26 thf(f9,plain,(
% 0.09/0.26 ~ ? [X0 : (($i > $i > $o) > $i)] : ! [X1 : ($i > $i > $o)] : (? [X2 : $i,X3 : $i] : (X1 @ X3 @ X2) => (X1 @ (epsa @ X1) @ (X0 @ X1)))),
% 0.09/0.26 inference(rectify,[],[f4])).
% 0.09/0.26 thf(f10,plain,(
% 0.09/0.26 ~ ? [X0 : (($i > $i > $o) > $i)] : ! [X1 : ($i > $i > $o)] : (? [X2 : $i,X3 : $i] : ($true = ((X1 @ X3 @ X2))) => (((X1 @ (epsa @ X1) @ (X0 @ X1))) = $true))),
% 0.09/0.26 inference(fool_elimination,[],[f9])).
% 0.09/0.26 thf(f11,plain,(
% 0.09/0.26 ! [X0 : ($i > $o)] : ((((X0 @ (eps @ X0))) = $true) | ! [X1 : $i] : (((X0 @ X1)) != $true))),
% 0.09/0.26 inference(ennf_transformation,[],[f6])).
% 0.09/0.26 thf(f12,plain,(
% 0.09/0.26 ! [X0 : (($i > $i > $o) > $i)] : ? [X1 : ($i > $i > $o)] : ((((X1 @ (epsa @ X1) @ (X0 @ X1))) != $true) & ? [X2 : $i,X3 : $i] : ($true = ((X1 @ X3 @ X2))))),
% 0.09/0.26 inference(ennf_transformation,[],[f10])).
% 0.09/0.26 thf(f13,plain,(
% 0.09/0.26 ! [X0 : (($i > $i > $o) > $i)] : (($true != ((sK0 @ X0 @ (epsa @ (sK0 @ X0)) @ (X0 @ (sK0 @ X0))))) & ($true = ((sK0 @ X0 @ (sK2 @ X0) @ (sK1 @ X0)))))),
% 0.09/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP]),skolemize(X3,sK2 @ X0),skolemize(X3,sK2 @ X0),skolemize(X3,sK2 @ X0)],[f12])).
% 0.09/0.26 thf(f14,plain,(
% 0.09/0.26 (epsa = (^[Y0 : $i > $i > $o]: (eps @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.09/0.26 inference(cnf_transformation,[],[f8])).
% 0.09/0.26 thf(f15,plain,(
% 0.09/0.26 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ (eps @ X0))) = $true) | (((X0 @ X1)) != $true)) )),
% 0.09/0.26 inference(cnf_transformation,[],[f11])).
% 0.09/0.26 thf(f16,plain,(
% 0.09/0.26 ( ! [X0 : (($i > $i > $o) > $i)] : (($true = ((sK0 @ X0 @ (sK2 @ X0) @ (sK1 @ X0))))) )),
% 0.09/0.26 inference(cnf_transformation,[],[f13])).
% 0.09/0.26 thf(f17,plain,(
% 0.09/0.26 ( ! [X0 : (($i > $i > $o) > $i)] : (($true != ((sK0 @ X0 @ (epsa @ (sK0 @ X0)) @ (X0 @ (sK0 @ X0)))))) )),
% 0.09/0.26 inference(cnf_transformation,[],[f13])).
% 0.09/0.26 thf(f19,plain,(
% 0.09/0.26 (epsa = (^[Y0 : $i > $i > $o]: (eps @ (^[Y1 : $i]: (?? @ $i @ (Y0 @ Y1))))))),
% 0.09/0.26 inference(beta-eta_normalization,[],[f14])).
% 0.09/0.26 thf(f21,definition,(
% 0.09/0.26 spl3_1 <=> (epsa = (^[Y0 : $i > $i > $o]: (eps @ (^[Y1 : $i]: (?? @ $i @ (Y0 @ Y1))))))),
% 0.09/0.26 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 0.09/0.26 thf(f23,plain,(
% 0.09/0.26 (epsa = (^[Y0 : $i > $i > $o]: (eps @ (^[Y1 : $i]: (?? @ $i @ (Y0 @ Y1)))))) | ~spl3_1),
% 0.09/0.26 inference(avatar_component_clause,[],[f21])).
% 0.09/0.26 thf(f24,plain,(
% 0.09/0.26 spl3_1),
% 0.09/0.26 inference(avatar_split_clause,[],[f19,f21])).
% 0.09/0.26 thf(f37,plain,(
% 0.09/0.26 ( ! [X1 : ($i > $i > $o)] : ((((epsa @ X1)) = (((^[Y0 : $i > $i > $o]: (eps @ (^[Y1 : $i]: (?? @ $i @ (Y0 @ Y1))))) @ X1)))) ) | ~spl3_1),
% 0.09/0.26 inference(argument_congruence,[],[f23])).
% 0.09/0.26 thf(f38,plain,(
% 0.09/0.26 ( ! [X1 : ($i > $i > $o)] : ((((epsa @ X1)) = ((eps @ (^[Y0 : $i]: (?? @ $i @ (X1 @ Y0))))))) ) | ~spl3_1),
% 0.09/0.26 inference(beta-eta_normalization,[],[f37])).
% 0.09/0.26 thf(f53,plain,(
% 0.09/0.26 ( ! [X0 : ($i > $i > $o),X1 : $i] : (($true != (((^[Y0 : $i]: (?? @ $i @ (X0 @ Y0))) @ X1))) | ($true = (((^[Y0 : $i]: (?? @ $i @ (X0 @ Y0))) @ (epsa @ X0))))) ) | ~spl3_1),
% 0.09/0.26 inference(superposition,[],[f15,f38])).
% 0.09/0.26 thf(f54,plain,(
% 0.09/0.26 ( ! [X0 : ($i > $i > $o),X1 : $i] : (($true != ((?? @ $i @ (X0 @ X1)))) | ($true = ((?? @ $i @ (X0 @ (epsa @ X0)))))) ) | ~spl3_1),
% 0.09/0.26 inference(beta-eta_normalization,[],[f53])).
% 0.09/0.26 thf(f55,plain,(
% 0.09/0.26 ( ! [X2 : $i,X0 : ($i > $i > $o),X1 : $i] : ((((X0 @ X1 @ X2)) = $false) | ($true = ((?? @ $i @ (X0 @ (epsa @ X0)))))) ) | ~spl3_1),
% 0.09/0.26 inference(pi_proxy_clausification,[],[f54])).
% 0.09/0.26 thf(f56,plain,(
% 0.09/0.26 ( ! [X2 : $i,X0 : ($i > $i > $o),X1 : $i] : (($true = ((X0 @ (epsa @ X0) @ (sK4 @ X0)))) | (((X0 @ X1 @ X2)) = $false)) ) | ~spl3_1),
% 0.09/0.26 inference(sigma_proxy_clausification,[],[f55])).
% 0.09/0.26 thf(f87,plain,(
% 0.09/0.26 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($false = ((sK0 @ sK4 @ X0 @ X1)))) ) | ~spl3_1),
% 0.09/0.26 inference(superposition,[],[f17,f56])).
% 0.09/0.26 thf(f89,plain,(
% 0.09/0.26 ( ! [X0 : $i,X1 : $i] : (($false = ((sK0 @ sK4 @ X0 @ X1)))) ) | ~spl3_1),
% 0.09/0.26 inference(trivial_inequality_removal,[],[f87])).
% 0.09/0.26 thf(f121,plain,(
% 0.09/0.26 ($false = $true) | ~spl3_1),
% 0.09/0.26 inference(superposition,[],[f89,f16])).
% 0.09/0.26 thf(f138,plain,(
% 0.09/0.26 $false | ~spl3_1),
% 0.09/0.26 inference(trivial_inequality_removal,[],[f121])).
% 0.09/0.26 thf(f139,plain,(
% 0.09/0.26 ~spl3_1),
% 0.09/0.26 inference(avatar_contradiction_clause,[],[f138])).
% 0.09/0.26 cnf(s1, plain, spl3_1, inference(sat_conversion,[],[f24])).
% 0.09/0.26 cnf(s6, plain, ~spl3_1, inference(sat_conversion,[],[f139])).
% 0.09/0.26 cnf(s7, plain, $false, inference(rat,[],[s1,s6])).
% 0.09/0.26 thf(f142,plain,(
% 0.09/0.26 $false),
% 0.09/0.26 inference(avatar_sat_refutation,[],[s7])).
% 0.09/0.26 % SZS output end Proof for theBenchmark
% 0.09/0.26 % (3832928)------------------------------
% 0.09/0.26 % (3832928)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (3832928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (3832928)CaDiCaL version: 2.1.3
% 0.09/0.26 % (3832928)Termination reason: Refutation
% 0.09/0.26 % (3832928)Time elapsed: 0.006 s
% 0.09/0.26 % (3832928)Peak memory usage: 12 MB
% 0.09/0.26 % (3832928)Instructions burned: 8 (million)
% 0.09/0.26 % (3832920)Success in time 0.04 s
% 0.09/0.26 % Vampire exiting
%------------------------------------------------------------------------------