%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO031^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:46:19 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO031^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n020.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 16:24:19 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.23 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
% 0.21/0.27 % (1247567)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (1247586)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=3112616937: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)
% 0.21/0.27 % (1247586) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1247567-1247586"...
% 0.21/0.27 % (1247586)...printing done.
% 0.21/0.27 % (1247586)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% 0.21/0.27 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.27 thf(func_def_1, type, sK0: (($o > $o) > $o)).
% 0.21/0.27 thf(func_def_4, type, vNOT: ($o > $o)).
% 0.21/0.27 thf(func_def_5, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.27 thf(func_def_6, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.27 thf(f1,conjecture,(
% 0.21/0.27 ~ ! [X0 : ($o > $o)] : ? [X1 : $o] : (((X0 @ X1)) = X1)),
% 0.21/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.21/0.27 thf(f2,negated_conjecture,(
% 0.21/0.27 ~ ~ ! [X0 : ($o > $o)] : ? [X1 : $o] : (((X0 @ X1)) = X1)),
% 0.21/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.27 thf(f3,plain,(
% 0.21/0.27 ! [X0 : ($o > $o)] : ? [X1 : $o] : (((X0 @ X1)) = X1)),
% 0.21/0.27 inference(flattening,[],[f2])).
% 0.21/0.27 thf(f4,plain,(
% 0.21/0.27 ! [X0 : ($o > $o)] : (((sK0 @ X0)) = ((X0 @ (sK0 @ X0))))),
% 0.21/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK0 @ X0)],[f3])).
% 0.21/0.27 thf(f5,plain,(
% 0.21/0.27 ( ! [X0 : ($o > $o)] : ((((sK0 @ X0)) = ((X0 @ (sK0 @ X0))))) )),
% 0.21/0.27 inference(cnf_transformation,[],[f4])).
% 0.21/0.27 thf(f7,plain,(
% 0.21/0.27 ( ! [X0 : ($o > $o)] : (($false = ((X0 @ (sK0 @ X0)))) | ($true = ((sK0 @ X0)))) )),
% 0.21/0.27 inference(iff_proxy_clausification,[],[f5])).
% 0.21/0.27 thf(f8,plain,(
% 0.21/0.27 ( ! [X0 : ($o > $o)] : (($true = ((X0 @ (sK0 @ X0)))) | (((sK0 @ X0)) = $false)) )),
% 0.21/0.27 inference(iff_proxy_clausification,[],[f5])).
% 0.21/0.27 thf(f12,plain,(
% 0.21/0.27 ( ! [X1 : ($o > $o)] : (((((^[Y0 : $o]: (~ (X1 @ Y0))) @ (sK0 @ (^[Y0 : $o]: (~ (X1 @ Y0)))))) = $false) | ($true = ((sK0 @ (^[Y0 : $o]: (~ (X1 @ Y0))))))) )),
% 0.21/0.27 inference(primitive_instantiation,[],[f7])).
% 0.21/0.27 thf(f16,plain,(
% 0.21/0.27 ( ! [X1 : ($o > $o)] : ((((~ (X1 @ (sK0 @ (^[Y0 : $o]: (~ (X1 @ Y0))))))) = $false) | ($true = ((sK0 @ (^[Y0 : $o]: (~ (X1 @ Y0))))))) )),
% 0.21/0.27 inference(beta-eta_normalization,[],[f12])).
% 0.21/0.27 thf(f17,plain,(
% 0.21/0.27 ( ! [X1 : ($o > $o)] : (($true = ((X1 @ (sK0 @ (^[Y0 : $o]: (~ (X1 @ Y0))))))) | ($true = ((sK0 @ (^[Y0 : $o]: (~ (X1 @ Y0))))))) )),
% 0.21/0.27 inference(not_proxy_clausification,[],[f16])).
% 0.21/0.27 thf(f29,plain,(
% 0.21/0.27 ( ! [X0 : ($o > $o)] : (($true = ((X0 @ $true))) | (((sK0 @ X0)) = $false) | (((sK0 @ X0)) = $false)) )),
% 0.21/0.27 inference(fool_paramodulation,[],[f8])).
% 0.21/0.27 thf(f38,plain,(
% 0.21/0.27 ( ! [X0 : ($o > $o)] : ((((sK0 @ X0)) = $false) | ($true = ((X0 @ $true)))) )),
% 0.21/0.27 inference(duplicate_literal_removal,[],[f29])).
% 0.21/0.27 thf(f58,plain,(
% 0.21/0.27 ($true = ((sK0 @ (^[Y0 : $o]: (~ ((^[Y1 : $o]: (Y1)) @ Y0)))))) | ($true = (((^[Y0 : $o]: (Y0)) @ (sK0 @ (^[Y0 : $o]: (~ ((^[Y1 : $o]: (Y1)) @ Y0)))))))),
% 0.21/0.27 inference(primitive_instantiation,[],[f17])).
% 0.21/0.27 thf(f65,plain,(
% 0.21/0.27 ($true = ((sK0 @ ~))) | ($true = ((sK0 @ ~)))),
% 0.21/0.27 inference(beta-eta_normalization,[],[f58])).
% 0.21/0.27 thf(f66,plain,(
% 0.21/0.27 ($true = ((sK0 @ ~)))),
% 0.21/0.27 inference(duplicate_literal_removal,[],[f65])).
% 0.21/0.27 thf(f80,definition,(
% 0.21/0.27 spl1_3 <=> ($true = ((sK0 @ ~)))),
% 0.21/0.27 introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition])).
% 0.21/0.27 thf(f82,plain,(
% 0.21/0.27 ($true = ((sK0 @ ~))) | ~spl1_3),
% 0.21/0.27 inference(avatar_component_clause,[],[f80])).
% 0.21/0.27 thf(f83,plain,(
% 0.21/0.27 spl1_3),
% 0.21/0.27 inference(avatar_split_clause,[],[f66,f80])).
% 0.21/0.27 thf(f84,plain,(
% 0.21/0.27 ($true = ((~ $true))) | ($true = $false) | ~spl1_3),
% 0.21/0.27 inference(superposition,[],[f82,f38])).
% 0.21/0.27 thf(f95,plain,(
% 0.21/0.27 ($true = $false) | ($true = $false) | ~spl1_3),
% 0.21/0.27 inference(not_proxy_clausification,[],[f84])).
% 0.21/0.27 thf(f96,plain,(
% 0.21/0.27 ($true = $false) | ~spl1_3),
% 0.21/0.27 inference(duplicate_literal_removal,[],[f95])).
% 0.21/0.27 thf(f97,plain,(
% 0.21/0.27 $false | ~spl1_3),
% 0.21/0.27 inference(trivial_inequality_removal,[],[f96])).
% 0.21/0.27 thf(f98,plain,(
% 0.21/0.27 ~spl1_3),
% 0.21/0.27 inference(avatar_contradiction_clause,[],[f97])).
% 0.21/0.27 cnf(s3, plain, spl1_3, inference(sat_conversion,[],[f83])).
% 0.21/0.27 cnf(s6, plain, ~spl1_3, inference(sat_conversion,[],[f98])).
% 0.21/0.27 cnf(s7, plain, $false, inference(rat,[],[s3,s6])).
% 0.21/0.27 thf(f99,plain,(
% 0.21/0.27 $false),
% 0.21/0.27 inference(avatar_sat_refutation,[],[s7])).
% 0.21/0.27 % SZS output end Proof for theBenchmark
% 0.21/0.27 % (1247586)------------------------------
% 0.21/0.27 % (1247586)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (1247586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (1247586)CaDiCaL version: 2.1.3
% 0.21/0.27 % (1247586)Termination reason: Refutation
% 0.21/0.27 % (1247586)Time elapsed: 0.002 s
% 0.21/0.27 % (1247586)Peak memory usage: 13 MB
% 0.21/0.27 % (1247586)Instructions burned: 3 (million)
% 0.21/0.27 % (1247567)Success in time 0.032 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------