%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO557^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 08:48:25 AM UTC 2026
% Result : Theorem 0.24s 0.29s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO557^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n018.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 17:17:11 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.24/0.29 % (373125)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.29 % (373152)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.29 % (373152)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
% 0.24/0.29 % (373152)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=3292291977:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.24/0.29 % (373152) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-373125-373152"...
% 0.24/0.29 % (373152)...printing done.
% 0.24/0.29 % (373152)Refutation found. Thanks to Tanya!
% 0.24/0.29 % SZS status Theorem for theBenchmark
% 0.24/0.29 % SZS output start Proof for theBenchmark
% 0.24/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.24/0.29 thf(func_def_0, type, eps: (($i > $o) > $i)).
% 0.24/0.29 thf(func_def_2, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.24/0.29 thf(func_def_3, type, db0: !>[X0: $tType]:(X0)).
% 0.24/0.29 thf(func_def_4, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.24/0.29 thf(func_def_7, type, sK0: ($i > $o)).
% 0.24/0.29 thf(f1,axiom,(
% 0.24/0.29 ! [X0 : ($i > $o)] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps @ X0)))),
% 0.24/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choiceax)).
% 0.24/0.29 thf(f2,conjecture,(
% 0.24/0.29 ((^[X0 : ($i > $o)] : ((X0 @ (eps @ X0)))) = (^[X0 : ($i > $o)] : ((?? @ $i @ X0))))),
% 0.24/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 0.24/0.29 thf(f3,negated_conjecture,(
% 0.24/0.29 ~ ((^[X0 : ($i > $o)] : ((X0 @ (eps @ X0)))) = (^[X0 : ($i > $o)] : ((?? @ $i @ X0))))),
% 0.24/0.29 inference(negated_conjecture,[status(cth)],[f2])).
% 0.24/0.29 thf(f4,plain,(
% 0.24/0.29 ~ ((^[X0 : ($i > $o)] : ((X0 @ (eps @ X0)))) = (^[X1 : ($i > $o)] : ((?? @ $i @ X1))))),
% 0.24/0.29 inference(rectify,[],[f3])).
% 0.24/0.29 thf(f5,plain,(
% 0.24/0.29 ~ ((^[Y0 : $i > $o]: (?? @ $i @ Y0)) = (^[Y0 : $i > $o]: (Y0 @ (eps @ Y0))))),
% 0.24/0.29 inference(fool_elimination,[],[f4])).
% 0.24/0.29 thf(f6,plain,(
% 0.24/0.29 ! [X0 : ($i > $o)] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps @ X0)))),
% 0.24/0.29 inference(rectify,[],[f1])).
% 0.24/0.29 thf(f7,plain,(
% 0.24/0.29 ! [X0 : ($i > $o)] : (? [X1 : $i] : (((X0 @ X1)) = $true) => (((X0 @ (eps @ X0))) = $true))),
% 0.24/0.29 inference(fool_elimination,[],[f6])).
% 0.24/0.29 thf(f8,plain,(
% 0.24/0.29 ((^[Y0 : $i > $o]: (?? @ $i @ Y0)) != (^[Y0 : $i > $o]: (Y0 @ (eps @ Y0))))),
% 0.24/0.29 inference(flattening,[],[f5])).
% 0.24/0.29 thf(f9,plain,(
% 0.24/0.29 ! [X0 : ($i > $o)] : (! [X1 : $i] : (((X0 @ X1)) != $true) | (((X0 @ (eps @ X0))) = $true))),
% 0.24/0.29 inference(ennf_transformation,[],[f7])).
% 0.24/0.29 thf(f10,plain,(
% 0.24/0.29 ((^[Y0 : $i > $o]: (?? @ $i @ Y0)) != (^[Y0 : $i > $o]: (Y0 @ (eps @ Y0))))),
% 0.24/0.29 inference(cnf_transformation,[],[f8])).
% 0.24/0.29 thf(f11,plain,(
% 0.24/0.29 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ (eps @ X0))) = $true) | (((X0 @ X1)) != $true)) )),
% 0.24/0.29 inference(cnf_transformation,[],[f9])).
% 0.24/0.29 thf(f13,definition,(
% 0.24/0.29 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.24/0.29 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.24/0.29 thf(f14,plain,(
% 0.24/0.29 (?? @ $i != (^[Y0 : $i > $o]: (Y0 @ (eps @ Y0))))),
% 0.24/0.29 inference(beta-eta_normalization,[],[f10])).
% 0.24/0.29 thf(f15,plain,(
% 0.24/0.29 ((((^[Y0 : $i > $o]: (Y0 @ (eps @ Y0))) @ sK0)) != ((?? @ $i @ sK0)))),
% 0.24/0.29 inference(negative_extensionality,[],[f14])).
% 0.24/0.29 thf(f16,plain,(
% 0.24/0.29 ($true = ((?? @ $i @ sK0))) | ((((^[Y0 : $i > $o]: (Y0 @ (eps @ Y0))) @ sK0)) = $true)),
% 0.24/0.29 inference(xor_proxy_clausification,[],[f15])).
% 0.24/0.29 thf(f17,plain,(
% 0.24/0.29 ($false = ((?? @ $i @ sK0))) | ((((^[Y0 : $i > $o]: (Y0 @ (eps @ Y0))) @ sK0)) = $false)),
% 0.24/0.29 inference(xor_proxy_clausification,[],[f15])).
% 0.24/0.29 thf(f18,plain,(
% 0.24/0.29 ( ! [X1 : $i] : (((((^[Y0 : $i > $o]: (Y0 @ (eps @ Y0))) @ sK0)) = $false) | ($false = ((sK0 @ X1)))) )),
% 0.24/0.29 inference(pi_proxy_clausification,[],[f17])).
% 0.24/0.29 thf(f19,plain,(
% 0.24/0.29 ( ! [X1 : $i] : ((((sK0 @ (eps @ sK0))) = $false) | ($false = ((sK0 @ X1)))) )),
% 0.24/0.29 inference(beta-eta_normalization,[],[f18])).
% 0.24/0.29 thf(f20,plain,(
% 0.24/0.29 (((sK0 @ sK1)) = $true) | ((((^[Y0 : $i > $o]: (Y0 @ (eps @ Y0))) @ sK0)) = $true)),
% 0.24/0.29 inference(sigma_proxy_clausification,[],[f16])).
% 0.24/0.29 thf(f21,plain,(
% 0.24/0.29 (((sK0 @ (eps @ sK0))) = $true) | (((sK0 @ sK1)) = $true)),
% 0.24/0.29 inference(beta-eta_normalization,[],[f20])).
% 0.24/0.29 thf(f23,definition,(
% 0.24/0.29 spl2_1 <=> (((sK0 @ (eps @ sK0))) = $false)),
% 0.24/0.29 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.24/0.29 thf(f25,plain,(
% 0.24/0.29 (((sK0 @ (eps @ sK0))) = $false) | ~spl2_1),
% 0.24/0.29 inference(avatar_component_clause,[],[f23])).
% 0.24/0.29 thf(f27,definition,(
% 0.24/0.29 spl2_2 <=> ! [X1 : $i] : ($false = ((sK0 @ X1)))),
% 0.24/0.29 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.24/0.29 thf(f28,plain,(
% 0.24/0.29 ( ! [X1 : $i] : (($false = ((sK0 @ X1)))) ) | ~spl2_2),
% 0.24/0.29 inference(avatar_component_clause,[],[f27])).
% 0.24/0.29 thf(f29,plain,(
% 0.24/0.29 spl2_1 | spl2_2),
% 0.24/0.29 inference(avatar_split_clause,[],[f19,f27,f23])).
% 0.24/0.29 thf(f31,definition,(
% 0.24/0.29 spl2_3 <=> (((sK0 @ (eps @ sK0))) = $true)),
% 0.24/0.29 introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition])).
% 0.24/0.29 thf(f33,plain,(
% 0.24/0.29 (((sK0 @ (eps @ sK0))) = $true) | ~spl2_3),
% 0.24/0.29 inference(avatar_component_clause,[],[f31])).
% 0.24/0.29 thf(f35,definition,(
% 0.24/0.29 spl2_4 <=> (((sK0 @ sK1)) = $true)),
% 0.24/0.29 introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition])).
% 0.24/0.29 thf(f37,plain,(
% 0.24/0.29 (((sK0 @ sK1)) = $true) | ~spl2_4),
% 0.24/0.29 inference(avatar_component_clause,[],[f35])).
% 0.24/0.29 thf(f38,plain,(
% 0.24/0.29 spl2_3 | spl2_4),
% 0.24/0.29 inference(avatar_split_clause,[],[f21,f35,f31])).
% 0.24/0.29 thf(f39,plain,(
% 0.24/0.29 ($true = $false) | (~spl2_2 | ~spl2_3)),
% 0.24/0.29 inference(forward_demodulation,[],[f33,f28])).
% 0.24/0.29 thf(f40,plain,(
% 0.24/0.29 $false | (~spl2_2 | ~spl2_3)),
% 0.24/0.29 inference(trivial_inequality_removal,[],[f39])).
% 0.24/0.29 thf(f41,plain,(
% 0.24/0.29 ~spl2_2 | ~spl2_3),
% 0.24/0.29 inference(avatar_contradiction_clause,[],[f40])).
% 0.24/0.29 thf(f45,plain,(
% 0.24/0.29 ($true = $false) | (~spl2_2 | ~spl2_4)),
% 0.24/0.29 inference(forward_demodulation,[],[f37,f28])).
% 0.24/0.29 thf(f46,plain,(
% 0.24/0.29 $false | (~spl2_2 | ~spl2_4)),
% 0.24/0.29 inference(trivial_inequality_removal,[],[f45])).
% 0.24/0.29 thf(f47,plain,(
% 0.24/0.29 ~spl2_2 | ~spl2_4),
% 0.24/0.29 inference(avatar_contradiction_clause,[],[f46])).
% 0.24/0.29 thf(f59,plain,(
% 0.24/0.29 ( ! [X0 : $i] : (($true != ((sK0 @ X0))) | ($true = $false)) ) | ~spl2_1),
% 0.24/0.29 inference(constrained_superposition,[],[f25,f11])).
% 0.24/0.29 thf(f60,plain,(
% 0.24/0.29 ( ! [X0 : $i] : (($true != ((sK0 @ X0)))) ) | ~spl2_1),
% 0.24/0.29 inference(trivial_inequality_removal,[],[f59])).
% 0.24/0.29 thf(f65,plain,(
% 0.24/0.29 ( ! [X0 : $i] : (($true != $true) | ($false = ((sK0 @ X0)))) ) | ~spl2_1),
% 0.24/0.29 inference(constrained_superposition,[],[f60,f13])).
% 0.24/0.29 thf(f69,plain,(
% 0.24/0.29 ( ! [X0 : $i] : (($false = ((sK0 @ X0)))) ) | ~spl2_1),
% 0.24/0.29 inference(trivial_inequality_removal,[],[f65])).
% 0.24/0.29 thf(f70,plain,(
% 0.24/0.29 spl2_2 | ~spl2_1),
% 0.24/0.29 inference(avatar_split_clause,[],[f69,f23,f27])).
% 0.24/0.29 cnf(s1, plain, spl2_1 | spl2_2, inference(sat_conversion,[],[f29])).
% 0.24/0.29 cnf(s2, plain, spl2_3 | spl2_4, inference(sat_conversion,[],[f38])).
% 0.24/0.29 cnf(s3, plain, ~spl2_2 | ~spl2_3, inference(sat_conversion,[],[f41])).
% 0.24/0.29 cnf(s5, plain, ~spl2_2 | ~spl2_4, inference(sat_conversion,[],[f47])).
% 0.24/0.29 cnf(s7, plain, ~spl2_1 | spl2_2, inference(sat_conversion,[],[f70])).
% 0.24/0.29 cnf(s8, plain, ~spl2_2, inference(rat,[],[s2,s3,s5])).
% 0.24/0.29 cnf(s9, plain, ~spl2_1, inference(rat,[],[s7,s8])).
% 0.24/0.29 cnf(s10, plain, $false, inference(rat,[],[s1,s8,s9])).
% 0.24/0.29 thf(f71,plain,(
% 0.24/0.29 $false),
% 0.24/0.29 inference(avatar_sat_refutation,[],[s10])).
% 0.24/0.29 % SZS output end Proof for theBenchmark
% 0.24/0.29 % (373152)------------------------------
% 0.24/0.29 % (373152)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.29 % (373152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.29 % (373152)CaDiCaL version: 2.1.3
% 0.24/0.29 % (373152)Termination reason: Refutation
% 0.24/0.29 % (373152)Time elapsed: 0.002 s
% 0.24/0.29 % (373152)Peak memory usage: 13 MB
% 0.24/0.29 % (373152)Instructions burned: 3 (million)
% 0.24/0.29 % (373125)Success in time 0.036 s
% 0.24/0.29 % Vampire exiting
%------------------------------------------------------------------------------