%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET616^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 08:23:43 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET616^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n015.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 13:42:48 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.26 % (3538902)Will run a generic schedule for satisfiability detection.
% 0.08/0.26 % (3538909)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1053972031_3000 on theBenchmark for (3000ds/0Mi)
% 0.08/0.26 % Exception at run slice level
% 0.08/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.26 % (3538912)dis+10_1_sil=32000:sp=arity:random_seed=2727995575:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.08/0.26 % (3538910)% WARNING: option uhcvi not known.
% 0.08/0.26 % (3538911)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=796005384:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.08/0.26 % (3538915)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=562984462:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.08/0.26 % (3538913)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1241641958:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.08/0.26 % (3538914)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3883987155:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.08/0.26 % (3538913)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.26 % (3538920)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=511414518:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.08/0.26 % Exception at run slice level% (3538915) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3538902-3538915"...
% 0.08/0.26
% 0.08/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.26 % (3538912) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3538902-3538912"...
% 0.08/0.26 % (3538913) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3538902-3538913"...
% 0.08/0.26 % (3538914) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3538902-3538914"...
% 0.08/0.26 % (3538910)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1027878334:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.08/0.26 % (3538911) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3538902-3538911"...
% 0.08/0.26 % (3538910)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.26 % (3538910)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.26 % (3538915)...printing done.
% 0.08/0.26 % (3538912)...printing done.
% 0.08/0.26 % (3538913)...printing done.
% 0.08/0.26 % (3538914)...printing done.
% 0.08/0.26 % (3538911)...printing done.
% 0.08/0.26 % (3538913)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% 0.08/0.26 thf(type_def_5, type, a: $tType).
% 0.08/0.26 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.26 thf(func_def_1, type, vAND: ($o > $o > $o)).
% 0.08/0.26 thf(func_def_2, type, db0: !>[X0: $tType]:(X0)).
% 0.08/0.26 thf(func_def_3, type, vNOT: ($o > $o)).
% 0.08/0.26 thf(func_def_4, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.08/0.26 thf(func_def_5, type, sK0: (a > $o)).
% 0.08/0.26 thf(func_def_6, type, sK1: (a > $o)).
% 0.08/0.26 thf(func_def_9, type, sK2: a).
% 0.08/0.26 thf(f1,conjecture,(
% 0.08/0.26 ! [X0 : (a > $o),X1 : (a > $o)] : (((^[X2 : a] : (~(X1 @ X2) & (X0 @ X2))) = (^[X2 : a] : (~(X0 @ X2) & (X1 @ X2)))) => (X0 = X1))),
% 0.08/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_90_pme)).
% 0.08/0.26 thf(f2,negated_conjecture,(
% 0.08/0.26 ~ ! [X0 : (a > $o),X1 : (a > $o)] : (((^[X2 : a] : (~(X1 @ X2) & (X0 @ X2))) = (^[X2 : a] : (~(X0 @ X2) & (X1 @ X2)))) => (X0 = X1))),
% 0.08/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.08/0.26 thf(f3,plain,(
% 0.08/0.26 ~ ! [X0 : (a > $o),X1 : (a > $o)] : (((^[X2 : a] : (~(X1 @ X2) & (X0 @ X2))) = (^[X3 : a] : (~(X0 @ X3) & (X1 @ X3)))) => (X0 = X1))),
% 0.08/0.26 inference(rectify,[],[f2])).
% 0.08/0.26 thf(f4,plain,(
% 0.08/0.26 ~ ! [X0 : (a > $o),X1 : (a > $o)] : (((^[Y0 : a]: ((X0 @ Y0) & (~ (X1 @ Y0)))) = (^[Y0 : a]: ((X1 @ Y0) & (~ (X0 @ Y0))))) => (X0 = X1))),
% 0.08/0.26 inference(fool_elimination,[],[f3])).
% 0.08/0.26 thf(f5,plain,(
% 0.08/0.26 ? [X0 : (a > $o),X1 : (a > $o)] : ((X0 != X1) & ((^[Y0 : a]: ((X0 @ Y0) & (~ (X1 @ Y0)))) = (^[Y0 : a]: ((X1 @ Y0) & (~ (X0 @ Y0))))))),
% 0.08/0.26 inference(ennf_transformation,[],[f4])).
% 0.08/0.26 thf(f6,plain,(
% 0.08/0.26 (sK0 != sK1) & ((^[Y0 : a]: ((sK0 @ Y0) & (~ (sK1 @ Y0)))) = (^[Y0 : a]: ((sK1 @ Y0) & (~ (sK0 @ Y0)))))),
% 0.08/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f5])).
% 0.08/0.26 thf(f7,plain,(
% 0.08/0.26 ((^[Y0 : a]: ((sK0 @ Y0) & (~ (sK1 @ Y0)))) = (^[Y0 : a]: ((sK1 @ Y0) & (~ (sK0 @ Y0)))))),
% 0.08/0.26 inference(cnf_transformation,[],[f6])).
% 0.08/0.26 thf(f8,plain,(
% 0.08/0.26 (sK0 != sK1)),
% 0.08/0.26 inference(cnf_transformation,[],[f6])).
% 0.08/0.26 thf(f10,definition,(
% 0.08/0.26 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.08/0.26 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.08/0.26 thf(f11,plain,(
% 0.08/0.26 (((sK0 @ sK2)) != ((sK1 @ sK2)))),
% 0.08/0.26 inference(negative_extensionality,[],[f8])).
% 0.08/0.26 thf(f12,plain,(
% 0.08/0.26 ($true = ((sK0 @ sK2))) | ($true = ((sK1 @ sK2)))),
% 0.08/0.26 inference(xor_proxy_clausification,[],[f11])).
% 0.08/0.26 thf(f13,plain,(
% 0.08/0.26 ($false = ((sK0 @ sK2))) | ($false = ((sK1 @ sK2)))),
% 0.08/0.26 inference(xor_proxy_clausification,[],[f11])).
% 0.08/0.26 thf(f15,definition,(
% 0.08/0.26 spl3_1 <=> ($false = ((sK1 @ sK2)))),
% 0.08/0.26 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 0.08/0.26 thf(f17,plain,(
% 0.08/0.26 ($false = ((sK1 @ sK2))) | ~spl3_1),
% 0.08/0.26 inference(avatar_component_clause,[],[f15])).
% 0.08/0.26 thf(f19,definition,(
% 0.08/0.26 spl3_2 <=> ($false = ((sK0 @ sK2)))),
% 0.08/0.26 introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition])).
% 0.08/0.26 thf(f20,plain,(
% 0.08/0.26 ($false != ((sK0 @ sK2))) | spl3_2),
% 0.08/0.26 inference(avatar_component_clause,[],[f19])).
% 0.08/0.26 thf(f21,plain,(
% 0.08/0.26 ($false = ((sK0 @ sK2))) | ~spl3_2),
% 0.08/0.26 inference(avatar_component_clause,[],[f19])).
% 0.08/0.26 thf(f22,plain,(
% 0.08/0.26 spl3_1 | spl3_2),
% 0.08/0.26 inference(avatar_split_clause,[],[f13,f19,f15])).
% 0.08/0.26 thf(f24,definition,(
% 0.08/0.26 spl3_3 <=> ($true = ((sK1 @ sK2)))),
% 0.08/0.26 introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition])).
% 0.08/0.26 thf(f25,plain,(
% 0.08/0.26 ($true != ((sK1 @ sK2))) | spl3_3),
% 0.08/0.26 inference(avatar_component_clause,[],[f24])).
% 0.08/0.26 thf(f26,plain,(
% 0.08/0.26 ($true = ((sK1 @ sK2))) | ~spl3_3),
% 0.08/0.26 inference(avatar_component_clause,[],[f24])).
% 0.08/0.26 thf(f28,definition,(
% 0.08/0.26 spl3_4 <=> ($true = ((sK0 @ sK2)))),
% 0.08/0.26 introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition])).
% 0.08/0.26 thf(f30,plain,(
% 0.08/0.26 ($true = ((sK0 @ sK2))) | ~spl3_4),
% 0.08/0.26 inference(avatar_component_clause,[],[f28])).
% 0.08/0.26 thf(f31,plain,(
% 0.08/0.26 spl3_3 | spl3_4),
% 0.08/0.26 inference(avatar_split_clause,[],[f12,f28,f24])).
% 0.08/0.26 thf(f32,plain,(
% 0.08/0.26 ( ! [X1 : a] : (((((^[Y0 : a]: ((sK0 @ Y0) & (~ (sK1 @ Y0)))) @ X1)) = (((^[Y0 : a]: ((sK1 @ Y0) & (~ (sK0 @ Y0)))) @ X1)))) )),
% 0.08/0.26 inference(argument_congruence,[],[f7])).
% 0.08/0.26 thf(f33,plain,(
% 0.08/0.26 ( ! [X1 : a] : (($true = (((^[Y0 : a]: ((sK0 @ Y0) & (~ (sK1 @ Y0)))) @ X1))) | ($false = (((^[Y0 : a]: ((sK1 @ Y0) & (~ (sK0 @ Y0)))) @ X1)))) )),
% 0.08/0.26 inference(iff_proxy_clausification,[],[f32])).
% 0.08/0.26 thf(f34,plain,(
% 0.08/0.26 ( ! [X1 : a] : (($false = (((^[Y0 : a]: ((sK0 @ Y0) & (~ (sK1 @ Y0)))) @ X1))) | ($true = (((^[Y0 : a]: ((sK1 @ Y0) & (~ (sK0 @ Y0)))) @ X1)))) )),
% 0.08/0.26 inference(iff_proxy_clausification,[],[f32])).
% 0.08/0.26 thf(f35,plain,(
% 0.08/0.26 ( ! [X1 : a] : (($false = (((sK0 @ X1) & (~ (sK1 @ X1))))) | ($true = (((sK1 @ X1) & (~ (sK0 @ X1)))))) )),
% 0.08/0.26 inference(beta-eta_normalization,[],[f34])).
% 0.08/0.26 thf(f36,plain,(
% 0.08/0.26 ( ! [X1 : a] : (($false = ((~ (sK1 @ X1)))) | ($true = (((sK1 @ X1) & (~ (sK0 @ X1))))) | ($false = ((sK0 @ X1)))) )),
% 0.08/0.26 inference(and_proxy_clausification,[],[f35])).
% 0.08/0.26 thf(f37,plain,(
% 0.08/0.26 ( ! [X1 : a] : (($true = ((sK1 @ X1))) | ($true = (((sK1 @ X1) & (~ (sK0 @ X1))))) | ($false = ((sK0 @ X1)))) )),
% 0.08/0.26 inference(not_proxy_clausification,[],[f36])).
% 0.08/0.26 thf(f39,plain,(
% 0.08/0.26 ( ! [X1 : a] : (($true = ((sK1 @ X1))) | ($true = ((sK1 @ X1))) | ($false = ((sK0 @ X1)))) )),
% 0.08/0.26 inference(and_proxy_clausification,[],[f37])).
% 0.08/0.26 thf(f40,plain,(
% 0.08/0.26 ( ! [X1 : a] : (($true = ((sK1 @ X1))) | ($false = ((sK0 @ X1)))) )),
% 0.08/0.26 inference(duplicate_literal_removal,[],[f39])).
% 0.08/0.26 thf(f43,plain,(
% 0.08/0.26 ( ! [X1 : a] : (($true = (((sK0 @ X1) & (~ (sK1 @ X1))))) | ($false = (((sK1 @ X1) & (~ (sK0 @ X1)))))) )),
% 0.08/0.26 inference(beta-eta_normalization,[],[f33])).
% 0.08/0.26 thf(f45,plain,(
% 0.08/0.26 ( ! [X1 : a] : (($true = ((sK0 @ X1))) | ($false = (((sK1 @ X1) & (~ (sK0 @ X1)))))) )),
% 0.08/0.26 inference(and_proxy_clausification,[],[f43])).
% 0.08/0.26 thf(f46,plain,(
% 0.08/0.26 ( ! [X1 : a] : (($true = ((sK0 @ X1))) | ($false = ((~ (sK0 @ X1)))) | ($false = ((sK1 @ X1)))) )),
% 0.08/0.26 inference(and_proxy_clausification,[],[f45])).
% 0.08/0.26 thf(f47,plain,(
% 0.08/0.26 ( ! [X1 : a] : (($true = ((sK0 @ X1))) | ($true = ((sK0 @ X1))) | ($false = ((sK1 @ X1)))) )),
% 0.08/0.26 inference(not_proxy_clausification,[],[f46])).
% 0.08/0.26 thf(f48,plain,(
% 0.08/0.26 ( ! [X1 : a] : (($false = ((sK1 @ X1))) | ($true = ((sK0 @ X1)))) )),
% 0.08/0.26 inference(duplicate_literal_removal,[],[f47])).
% 0.08/0.26 thf(f65,plain,(
% 0.08/0.26 ($true = $false) | ($true = ((sK0 @ sK2))) | ~spl3_3),
% 0.08/0.26 inference(constrained_superposition,[],[f26,f48])).
% 0.08/0.26 thf(f68,plain,(
% 0.08/0.26 ($true = ((sK0 @ sK2))) | ~spl3_3),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f65])).
% 0.08/0.26 thf(f72,plain,(
% 0.08/0.26 ($true = $false) | (~spl3_2 | ~spl3_3)),
% 0.08/0.26 inference(forward_demodulation,[],[f68,f21])).
% 0.08/0.26 thf(f73,plain,(
% 0.08/0.26 $false | (~spl3_2 | ~spl3_3)),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f72])).
% 0.08/0.26 thf(f74,plain,(
% 0.08/0.26 ~spl3_2 | ~spl3_3),
% 0.08/0.26 inference(avatar_contradiction_clause,[],[f73])).
% 0.08/0.26 thf(f80,plain,(
% 0.08/0.26 ($true = $false) | (~spl3_1 | ~spl3_3)),
% 0.08/0.26 inference(constrained_superposition,[],[f17,f26])).
% 0.08/0.26 thf(f81,plain,(
% 0.08/0.26 ($true = $false) | ($false = ((sK0 @ sK2))) | ~spl3_1),
% 0.08/0.26 inference(constrained_superposition,[],[f17,f40])).
% 0.08/0.26 thf(f87,plain,(
% 0.08/0.26 ($false = ((sK0 @ sK2))) | ~spl3_1),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f81])).
% 0.08/0.26 thf(f88,plain,(
% 0.08/0.26 $false | (~spl3_1 | ~spl3_3)),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f80])).
% 0.08/0.26 thf(f89,plain,(
% 0.08/0.26 ~spl3_1 | ~spl3_3),
% 0.08/0.26 inference(avatar_contradiction_clause,[],[f88])).
% 0.08/0.26 thf(f93,plain,(
% 0.08/0.26 $false | (~spl3_1 | spl3_2)),
% 0.08/0.26 inference(forward_subsumption_resolution,[],[f87,f20])).
% 0.08/0.26 thf(f94,plain,(
% 0.08/0.26 ~spl3_1 | spl3_2),
% 0.08/0.26 inference(avatar_contradiction_clause,[],[f93])).
% 0.08/0.26 thf(f97,plain,(
% 0.08/0.26 ($true != $true) | ($false = ((sK1 @ sK2))) | spl3_3),
% 0.08/0.26 inference(constrained_superposition,[],[f25,f10])).
% 0.08/0.26 thf(f101,plain,(
% 0.08/0.26 ($false = ((sK1 @ sK2))) | spl3_3),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f97])).
% 0.08/0.26 thf(f102,plain,(
% 0.08/0.26 spl3_1 | spl3_3),
% 0.08/0.26 inference(avatar_split_clause,[],[f101,f24,f15])).
% 0.08/0.26 thf(f110,plain,(
% 0.08/0.26 ($true = $false) | (~spl3_2 | ~spl3_4)),
% 0.08/0.26 inference(constrained_superposition,[],[f30,f21])).
% 0.08/0.26 thf(f114,plain,(
% 0.08/0.26 $false | (~spl3_2 | ~spl3_4)),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f110])).
% 0.08/0.26 thf(f115,plain,(
% 0.08/0.26 ~spl3_2 | ~spl3_4),
% 0.08/0.26 inference(avatar_contradiction_clause,[],[f114])).
% 0.08/0.26 cnf(s1, plain, spl3_1 | spl3_2, inference(sat_conversion,[],[f22])).
% 0.08/0.26 cnf(s2, plain, spl3_3 | spl3_4, inference(sat_conversion,[],[f31])).
% 0.08/0.26 cnf(s3, plain, ~spl3_2 | ~spl3_3, inference(sat_conversion,[],[f74])).
% 0.08/0.26 cnf(s8, plain, ~spl3_1 | ~spl3_3, inference(sat_conversion,[],[f89])).
% 0.08/0.26 cnf(s10, plain, ~spl3_1 | spl3_2, inference(sat_conversion,[],[f94])).
% 0.08/0.26 cnf(s11, plain, spl3_1 | spl3_3, inference(sat_conversion,[],[f102])).
% 0.08/0.26 cnf(s13, plain, ~spl3_2 | ~spl3_4, inference(sat_conversion,[],[f115])).
% 0.08/0.26 cnf(s14, plain, spl3_1, inference(rat,[],[s3,s1,s11])).
% 0.08/0.26 cnf(s15, plain, spl3_2, inference(rat,[],[s10,s14])).
% 0.08/0.26 cnf(s16, plain, ~spl3_3, inference(rat,[],[s8,s14])).
% 0.08/0.26 cnf(s17, plain, ~spl3_4, inference(rat,[],[s13,s15])).
% 0.08/0.26 cnf(s18, plain, $false, inference(rat,[],[s2,s17,s16])).
% 0.08/0.26 thf(f116,plain,(
% 0.08/0.26 $false),
% 0.08/0.26 inference(avatar_sat_refutation,[],[s18])).
% 0.08/0.26 % SZS output end Proof for theBenchmark
% 0.08/0.26 % (3538913)------------------------------
% 0.08/0.26 % (3538913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (3538913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (3538913)CaDiCaL version: 2.1.3
% 0.08/0.26 % (3538913)Termination reason: Refutation
% 0.08/0.26 % (3538913)Time elapsed: 0.004 s
% 0.08/0.26 % (3538913)Peak memory usage: 12 MB
% 0.08/0.26 % (3538913)Instructions burned: 5 (million)
% 0.08/0.26 % (3538902)Success in time 0.028 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------