%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO277^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 08:47:20 AM UTC 2026
% Result : Theorem 0.36s 0.45s
% Output : Refutation 0.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYO277^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.27/0.31 % Computer : n003.cluster.edu
% 0.27/0.31 % Model : x86_64 x86_64
% 0.27/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.27/0.31 % Memory : 8046.5625MB
% 0.27/0.31 % OS : Linux 6.8.0-71-generic
% 0.27/0.31 % CPULimit : 300
% 0.27/0.31 % WCLimit : 300
% 0.27/0.31 % DateTime : Tue Sep 29 16:44:29 UTC 2026
% 0.27/0.31 % CPUTime :
% 0.27/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.27/0.37 Running higher-order theorem proving
% 0.27/0.38 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
% 0.36/0.45 % (2729099)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.36/0.45 % (2729104)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4106326958:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.36/0.45 % (2729104) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2729099-2729104"...
% 0.36/0.45 % (2729104)...printing done.
% 0.36/0.45 % (2729104)Refutation found. Thanks to Tanya!
% 0.36/0.45 % SZS status Theorem for theBenchmark
% 0.36/0.45 % SZS output start Proof for theBenchmark
% 0.36/0.45 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.36/0.45 thf(func_def_5, type, sK2: ($i > $i > $o)).
% 0.36/0.45 thf(func_def_6, type, sK3: ($i > $o)).
% 0.36/0.45 thf(func_def_7, type, sK4: (($i > $i > $o) > $i)).
% 0.36/0.45 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.36/0.45 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.36/0.45 thf(func_def_11, type, db1: !>[X0: $tType]:(X0)).
% 0.36/0.45 thf(func_def_12, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.36/0.45 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.36/0.45 thf(f1,conjecture,(
% 0.36/0.45 ! [X1 : $i,X0 : $i] : (! [X3 : ($i > $i > $o)] : (! [X4 : $i] : (X3 @ X4 @ X4) => (X3 @ X0 @ X1)) <=> ! [X2 : ($i > $o)] : ((X2 @ X0) => (X2 @ X1)))),
% 0.36/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM47D)).
% 0.36/0.45 thf(f2,negated_conjecture,(
% 0.36/0.45 ~ ! [X1 : $i,X0 : $i] : (! [X3 : ($i > $i > $o)] : (! [X4 : $i] : (X3 @ X4 @ X4) => (X3 @ X0 @ X1)) <=> ! [X2 : ($i > $o)] : ((X2 @ X0) => (X2 @ X1)))),
% 0.36/0.45 inference(negated_conjecture,[status(cth)],[f1])).
% 0.36/0.45 thf(f3,plain,(
% 0.36/0.45 ~ ! [X0 : $i,X1 : $i] : (! [X2 : ($i > $i > $o)] : (! [X3 : $i] : (X2 @ X3 @ X3) => (X2 @ X1 @ X0)) <=> ! [X4 : ($i > $o)] : ((X4 @ X1) => (X4 @ X0)))),
% 0.36/0.45 inference(rectify,[],[f2])).
% 0.36/0.45 thf(f4,plain,(
% 0.36/0.45 ~ ! [X1 : $i,X0 : $i] : (! [X2 : ($i > $i > $o)] : (! [X3 : $i] : ($true = ((X2 @ X3 @ X3))) => (((X2 @ X1 @ X0)) = $true)) <=> ! [X4 : ($i > $o)] : ((((X4 @ X1)) = $true) => (((X4 @ X0)) = $true)))),
% 0.36/0.45 inference(fool_elimination,[],[f3])).
% 0.36/0.45 thf(f5,plain,(
% 0.36/0.45 ? [X0 : $i,X1 : $i] : (! [X4 : ($i > $o)] : ((((X4 @ X0)) = $true) | (((X4 @ X1)) != $true)) <~> ! [X2 : ($i > $i > $o)] : (? [X3 : $i] : ($true != ((X2 @ X3 @ X3))) | (((X2 @ X1 @ X0)) = $true)))),
% 0.36/0.45 inference(ennf_transformation,[],[f4])).
% 0.36/0.45 thf(f6,plain,(
% 0.36/0.45 ? [X0 : $i,X1 : $i] : ((? [X2 : ($i > $i > $o)] : (! [X3 : $i] : ($true = ((X2 @ X3 @ X3))) & (((X2 @ X1 @ X0)) != $true)) | ? [X4 : ($i > $o)] : ((((X4 @ X0)) != $true) & (((X4 @ X1)) = $true))) & (! [X2 : ($i > $i > $o)] : (? [X3 : $i] : ($true != ((X2 @ X3 @ X3))) | (((X2 @ X1 @ X0)) = $true)) | ! [X4 : ($i > $o)] : ((((X4 @ X0)) = $true) | (((X4 @ X1)) != $true))))),
% 0.36/0.45 inference(nnf_transformation,[],[f5])).
% 0.36/0.45 thf(f7,plain,(
% 0.36/0.45 ? [X0 : $i,X1 : $i] : ((? [X2 : ($i > $i > $o)] : (! [X3 : $i] : ($true = ((X2 @ X3 @ X3))) & (((X2 @ X1 @ X0)) != $true)) | ? [X4 : ($i > $o)] : ((((X4 @ X0)) != $true) & (((X4 @ X1)) = $true))) & (! [X5 : ($i > $i > $o)] : (? [X6 : $i] : (((X5 @ X6 @ X6)) != $true) | ($true = ((X5 @ X1 @ X0)))) | ! [X7 : ($i > $o)] : ((((X7 @ X0)) = $true) | ($true != ((X7 @ X1))))))),
% 0.36/0.45 inference(rectify,[],[f6])).
% 0.36/0.45 thf(f8,plain,(
% 0.36/0.45 ((! [X3 : $i] : (((sK2 @ X3 @ X3)) = $true) & ($true != ((sK2 @ sK1 @ sK0)))) | (($true != ((sK3 @ sK0))) & ($true = ((sK3 @ sK1))))) & (! [X5 : ($i > $i > $o)] : (($true != ((X5 @ (sK4 @ X5) @ (sK4 @ X5)))) | (((X5 @ sK1 @ sK0)) = $true)) | ! [X7 : ($i > $o)] : ((((X7 @ sK0)) = $true) | (((X7 @ sK1)) != $true)))),
% 0.36/0.45 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X4,sK3),skolemize(X6,sK4 @ X5)],[f7])).
% 0.36/0.45 thf(f9,plain,(
% 0.36/0.45 ( ! [X7 : ($i > $o),X5 : ($i > $i > $o)] : ((((X7 @ sK1)) != $true) | (((X7 @ sK0)) = $true) | ($true != ((X5 @ (sK4 @ X5) @ (sK4 @ X5)))) | (((X5 @ sK1 @ sK0)) = $true)) )),
% 0.36/0.45 inference(cnf_transformation,[],[f8])).
% 0.36/0.45 thf(f10,plain,(
% 0.36/0.45 ($true != ((sK2 @ sK1 @ sK0))) | ($true = ((sK3 @ sK1)))),
% 0.36/0.45 inference(cnf_transformation,[],[f8])).
% 0.36/0.45 thf(f11,plain,(
% 0.36/0.45 ($true != ((sK2 @ sK1 @ sK0))) | ($true != ((sK3 @ sK0)))),
% 0.36/0.45 inference(cnf_transformation,[],[f8])).
% 0.36/0.45 thf(f12,plain,(
% 0.36/0.45 ( ! [X3 : $i] : (($true = ((sK3 @ sK1))) | (((sK2 @ X3 @ X3)) = $true)) )),
% 0.36/0.45 inference(cnf_transformation,[],[f8])).
% 0.36/0.45 thf(f13,plain,(
% 0.36/0.45 ( ! [X3 : $i] : (($true != ((sK3 @ sK0))) | (((sK2 @ X3 @ X3)) = $true)) )),
% 0.36/0.45 inference(cnf_transformation,[],[f8])).
% 0.36/0.45 thf(f17,definition,(
% 0.36/0.45 spl5_1 <=> ($true = ((sK3 @ sK0)))),
% 0.36/0.45 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 0.36/0.45 thf(f19,plain,(
% 0.36/0.45 ($true != ((sK3 @ sK0))) | spl5_1),
% 0.36/0.45 inference(avatar_component_clause,[],[f17])).
% 0.36/0.45 thf(f21,definition,(
% 0.36/0.45 spl5_2 <=> ! [X3 : $i] : (((sK2 @ X3 @ X3)) = $true)),
% 0.36/0.45 introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition])).
% 0.36/0.45 thf(f22,plain,(
% 0.36/0.45 ( ! [X3 : $i] : ((((sK2 @ X3 @ X3)) = $true)) ) | ~spl5_2),
% 0.36/0.45 inference(avatar_component_clause,[],[f21])).
% 0.36/0.45 thf(f23,plain,(
% 0.36/0.45 ~spl5_1 | spl5_2),
% 0.36/0.45 inference(avatar_split_clause,[],[f13,f21,f17])).
% 0.36/0.45 thf(f25,definition,(
% 0.36/0.45 spl5_3 <=> ! [X5 : ($i > $i > $o)] : (($true != ((X5 @ (sK4 @ X5) @ (sK4 @ X5)))) | (((X5 @ sK1 @ sK0)) = $true))),
% 0.36/0.45 introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition])).
% 0.36/0.45 thf(f26,plain,(
% 0.36/0.45 ( ! [X5 : ($i > $i > $o)] : (($true != ((X5 @ (sK4 @ X5) @ (sK4 @ X5)))) | (((X5 @ sK1 @ sK0)) = $true)) ) | ~spl5_3),
% 0.36/0.45 inference(avatar_component_clause,[],[f25])).
% 0.36/0.45 thf(f28,definition,(
% 0.36/0.45 spl5_4 <=> ! [X7 : ($i > $o)] : ((((X7 @ sK1)) != $true) | (((X7 @ sK0)) = $true))),
% 0.36/0.45 introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition])).
% 0.36/0.45 thf(f29,plain,(
% 0.36/0.45 ( ! [X7 : ($i > $o)] : ((((X7 @ sK1)) != $true) | (((X7 @ sK0)) = $true)) ) | ~spl5_4),
% 0.36/0.45 inference(avatar_component_clause,[],[f28])).
% 0.36/0.45 thf(f30,plain,(
% 0.36/0.45 spl5_3 | spl5_4),
% 0.36/0.45 inference(avatar_split_clause,[],[f9,f28,f25])).
% 0.36/0.45 thf(f32,definition,(
% 0.36/0.45 spl5_5 <=> ($true = ((sK2 @ sK1 @ sK0)))),
% 0.36/0.45 introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition])).
% 0.36/0.45 thf(f34,plain,(
% 0.36/0.45 ($true != ((sK2 @ sK1 @ sK0))) | spl5_5),
% 0.36/0.45 inference(avatar_component_clause,[],[f32])).
% 0.36/0.45 thf(f35,plain,(
% 0.36/0.45 ~spl5_5 | ~spl5_1),
% 0.36/0.45 inference(avatar_split_clause,[],[f11,f17,f32])).
% 0.36/0.45 thf(f37,definition,(
% 0.36/0.45 spl5_6 <=> ($true = ((sK3 @ sK1)))),
% 0.36/0.45 introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition])).
% 0.36/0.45 thf(f39,plain,(
% 0.36/0.45 ($true = ((sK3 @ sK1))) | ~spl5_6),
% 0.36/0.45 inference(avatar_component_clause,[],[f37])).
% 0.36/0.45 thf(f40,plain,(
% 0.36/0.45 spl5_6 | ~spl5_5),
% 0.36/0.45 inference(avatar_split_clause,[],[f10,f32,f37])).
% 0.36/0.45 thf(f41,plain,(
% 0.36/0.45 spl5_6 | spl5_2),
% 0.36/0.45 inference(avatar_split_clause,[],[f12,f21,f37])).
% 0.36/0.45 thf(f42,plain,(
% 0.36/0.45 ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1)))) @ sK1 @ sK0))) | ($true != (((^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1)))) @ (sK4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1))))) @ (sK4 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1)))))))) | ~spl5_3),
% 0.36/0.45 inference(primitive_instantiation,[],[f26])).
% 0.36/0.45 thf(f48,plain,(
% 0.36/0.45 ($true != $true) | ($true = ((sK2 @ sK1 @ sK0))) | (~spl5_2 | ~spl5_3)),
% 0.36/0.45 inference(constrained_superposition,[],[f26,f22])).
% 0.36/0.45 thf(f54,plain,(
% 0.36/0.45 ($true = ((sK1 = sK0))) | ($true != (((sK4 @ =) = (sK4 @ =)))) | ~spl5_3),
% 0.36/0.45 inference(beta-eta_normalization,[],[f42])).
% 0.36/0.45 thf(f55,plain,(
% 0.36/0.45 ($true != (((sK4 @ =) = (sK4 @ =)))) | (sK1 = sK0) | ~spl5_3),
% 0.36/0.45 inference(equality_proxy_clausification,[],[f54])).
% 0.36/0.45 thf(f56,plain,(
% 0.36/0.45 (((sK4 @ =)) != ((sK4 @ =))) | (sK1 = sK0) | ~spl5_3),
% 0.36/0.45 inference(equality_proxy_clausification,[],[f55])).
% 0.36/0.45 thf(f57,plain,(
% 0.36/0.45 (sK1 = sK0) | ~spl5_3),
% 0.36/0.45 inference(trivial_inequality_removal,[],[f56])).
% 0.36/0.45 thf(f59,plain,(
% 0.36/0.45 ($true = ((sK2 @ sK1 @ sK0))) | (~spl5_2 | ~spl5_3)),
% 0.36/0.45 inference(trivial_inequality_removal,[],[f48])).
% 0.36/0.45 thf(f65,plain,(
% 0.36/0.45 $false | (~spl5_2 | ~spl5_3 | spl5_5)),
% 0.36/0.45 inference(forward_subsumption_resolution,[],[f59,f34])).
% 0.36/0.45 thf(f66,plain,(
% 0.36/0.45 ~spl5_2 | ~spl5_3 | spl5_5),
% 0.36/0.45 inference(avatar_contradiction_clause,[],[f65])).
% 0.36/0.45 thf(f68,plain,(
% 0.36/0.45 ($true = ((sK3 @ sK0))) | (~spl5_3 | ~spl5_6)),
% 0.36/0.45 inference(forward_demodulation,[],[f39,f57])).
% 0.36/0.45 thf(f69,plain,(
% 0.36/0.45 $false | (spl5_1 | ~spl5_3 | ~spl5_6)),
% 0.36/0.45 inference(forward_subsumption_resolution,[],[f68,f19])).
% 0.36/0.45 thf(f70,plain,(
% 0.36/0.45 spl5_1 | ~spl5_3 | ~spl5_6),
% 0.36/0.45 inference(avatar_contradiction_clause,[],[f69])).
% 0.36/0.45 thf(f71,plain,(
% 0.36/0.45 (sK1 = sK0) | ~spl5_4),
% 0.36/0.45 inference(leibniz_equality_elimination,[],[f29])).
% 0.36/0.45 thf(f77,plain,(
% 0.36/0.45 ($true = ((sK3 @ sK0))) | ($true != $true) | (~spl5_4 | ~spl5_6)),
% 0.36/0.45 inference(constrained_superposition,[],[f29,f39])).
% 0.36/0.45 thf(f79,plain,(
% 0.36/0.45 ($true = ((sK3 @ sK0))) | (~spl5_4 | ~spl5_6)),
% 0.36/0.45 inference(trivial_inequality_removal,[],[f77])).
% 0.36/0.45 thf(f88,plain,(
% 0.36/0.45 spl5_1 | ~spl5_4 | ~spl5_6),
% 0.36/0.45 inference(avatar_split_clause,[],[f79,f37,f28,f17])).
% 0.36/0.45 thf(f91,plain,(
% 0.36/0.45 ($true != ((sK2 @ sK0 @ sK0))) | (~spl5_4 | spl5_5)),
% 0.36/0.45 inference(constrained_superposition,[],[f34,f71])).
% 0.36/0.45 thf(f92,plain,(
% 0.36/0.45 $false | (~spl5_2 | ~spl5_4 | spl5_5)),
% 0.36/0.45 inference(forward_subsumption_resolution,[],[f91,f22])).
% 0.36/0.45 thf(f93,plain,(
% 0.36/0.45 ~spl5_2 | ~spl5_4 | spl5_5),
% 0.36/0.45 inference(avatar_contradiction_clause,[],[f92])).
% 0.36/0.45 cnf(s1, plain, ~spl5_1 | spl5_2, inference(sat_conversion,[],[f23])).
% 0.36/0.45 cnf(s2, plain, spl5_3 | spl5_4, inference(sat_conversion,[],[f30])).
% 0.36/0.45 cnf(s3, plain, ~spl5_1 | ~spl5_5, inference(sat_conversion,[],[f35])).
% 0.36/0.45 cnf(s4, plain, ~spl5_5 | spl5_6, inference(sat_conversion,[],[f40])).
% 0.36/0.45 cnf(s5, plain, spl5_2 | spl5_6, inference(sat_conversion,[],[f41])).
% 0.36/0.45 cnf(s6, plain, ~spl5_2 | ~spl5_3 | spl5_5, inference(sat_conversion,[],[f66])).
% 0.36/0.45 cnf(s7, plain, spl5_1 | ~spl5_3 | ~spl5_6, inference(sat_conversion,[],[f70])).
% 0.36/0.45 cnf(s9, plain, spl5_1 | ~spl5_4 | ~spl5_6, inference(sat_conversion,[],[f88])).
% 0.36/0.45 cnf(s10, plain, ~spl5_2 | ~spl5_4 | spl5_5, inference(sat_conversion,[],[f93])).
% 0.36/0.45 cnf(s11, plain, ~spl5_6 | spl5_1, inference(rat,[],[s2,s7,s9])).
% 0.36/0.45 cnf(s12, plain, ~spl5_2 | spl5_5, inference(rat,[],[s2,s6,s10])).
% 0.36/0.45 cnf(s13, plain, spl5_6, inference(rat,[],[s12,s4,s5])).
% 0.36/0.45 cnf(s14, plain, spl5_1, inference(rat,[],[s11,s13])).
% 0.36/0.45 cnf(s15, plain, ~spl5_5, inference(rat,[],[s3,s14])).
% 0.36/0.45 cnf(s16, plain, spl5_2, inference(rat,[],[s1,s14])).
% 0.36/0.45 cnf(s17, plain, $false, inference(rat,[],[s12,s15,s16])).
% 0.36/0.45 thf(f94,plain,(
% 0.36/0.45 $false),
% 0.36/0.45 inference(avatar_sat_refutation,[],[s17])).
% 0.36/0.45 % SZS output end Proof for theBenchmark
% 0.36/0.45 % (2729104)------------------------------
% 0.36/0.45 % (2729104)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.36/0.45 % (2729104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/0.45 % (2729104)CaDiCaL version: 2.1.3
% 0.36/0.45 % (2729104)Termination reason: Refutation
% 0.36/0.45 % (2729104)Time elapsed: 0.004 s
% 0.36/0.45 % (2729104)Peak memory usage: 13 MB
% 0.36/0.45 % (2729104)Instructions burned: 5 (million)
% 0.36/0.45 % (2729099)Success in time 0.051 s
% 0.36/0.45 % Vampire exiting
%------------------------------------------------------------------------------