%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU540^2 : 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 : n002.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 08:29:59 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU540^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.20 % Computer : n002.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.20 % CPULimit : 300
% 0.11/0.20 % WCLimit : 300
% 0.11/0.20 % DateTime : Tue Sep 29 13:51:37 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 Running higher-order theorem proving
% 0.11/0.24 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
% 0.21/0.28 % (1315908)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (1315916)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=3671720082: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)
% 0.21/0.28 % (1315916) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1315908-1315916"...
% 0.21/0.28 % (1315919)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.28 % (1315919)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
% 0.21/0.28 % (1315916)...printing done.
% 0.21/0.28 % (1315916)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% 0.21/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.28 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.21/0.28 thf(func_def_2, type, powerset: ($i > $i)).
% 0.21/0.28 thf(func_def_3, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.21/0.28 thf(func_def_4, type, dsetconstrI: $o).
% 0.21/0.28 thf(func_def_6, type, prop2set: ($o > $i)).
% 0.21/0.28 thf(func_def_7, type, powersetI: $o).
% 0.21/0.28 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.28 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.28 thf(func_def_12, type, db1: !>[X0: $tType]:(X0)).
% 0.21/0.28 thf(func_def_13, type, sK0: ($i > $i > $i)).
% 0.21/0.28 thf(func_def_16, type, sK3: $o).
% 0.21/0.28 thf(func_def_18, type, sK5: ($i > $o)).
% 0.21/0.28 thf(func_def_20, type, vNOT: ($o > $o)).
% 0.21/0.28 thf(f1,axiom,(
% 0.21/0.28 (dsetconstrI = ! [X1 : ($i > $o),X0 : $i,X2 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))))))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI)).
% 0.21/0.28 thf(f2,axiom,(
% 0.21/0.28 ((^[X0 : $o] : ((dsetconstr @ (powerset @ emptyset) @ (^[X1 : $i] : (X0))))) = prop2set)),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set)).
% 0.21/0.28 thf(f3,axiom,(
% 0.21/0.28 (powersetI = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI)).
% 0.21/0.28 thf(f4,conjecture,(
% 0.21/0.28 dsetconstrI => (powersetI => ! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0))))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI)).
% 0.21/0.28 thf(f5,negated_conjecture,(
% 0.21/0.28 ~(dsetconstrI => (powersetI => ! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0)))))),
% 0.21/0.28 inference(negated_conjecture,[status(cth)],[f4])).
% 0.21/0.28 thf(f6,plain,(
% 0.21/0.28 (dsetconstrI = ! [X0 : ($i > $o),X1 : $i,X2 : $i] : ((in @ X2 @ X1) => ((X0 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ (^[X3 : $i] : ((X0 @ X3))))))))),
% 0.21/0.28 inference(rectify,[],[f1])).
% 0.21/0.28 thf(f7,plain,(
% 0.21/0.28 (dsetconstrI = $true) <=> ! [X0 : ($i > $o),X2 : $i,X1 : $i] : ((((in @ X2 @ X1)) = $true) => ((((X0 @ X2)) = $true) => (((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true)))),
% 0.21/0.28 inference(fool_elimination,[],[f6])).
% 0.21/0.28 thf(f8,plain,(
% 0.21/0.28 ~(dsetconstrI => (powersetI => ! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0)))))),
% 0.21/0.28 inference(rectify,[],[f5])).
% 0.21/0.28 thf(f9,plain,(
% 0.21/0.28 ~((dsetconstrI = $true) => ((powersetI = $true) => ! [X0 : $o] : (($true = X0) => (((in @ emptyset @ (prop2set @ X0))) = $true))))),
% 0.21/0.28 inference(fool_elimination,[],[f8])).
% 0.21/0.28 thf(f10,plain,(
% 0.21/0.28 (powersetI = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))))),
% 0.21/0.28 inference(rectify,[],[f3])).
% 0.21/0.28 thf(f11,plain,(
% 0.21/0.28 (powersetI = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => (((in @ X1 @ (powerset @ X0))) = $true))),
% 0.21/0.28 inference(fool_elimination,[],[f10])).
% 0.21/0.28 thf(f12,plain,(
% 0.21/0.28 ((^[X0 : $o] : ((dsetconstr @ (powerset @ emptyset) @ (^[X1 : $i] : (X0))))) = prop2set)),
% 0.21/0.28 inference(rectify,[],[f2])).
% 0.21/0.28 thf(f13,plain,(
% 0.21/0.28 (prop2set = (^[Y0 : $o]: (dsetconstr @ (powerset @ emptyset) @ (^[Y1 : $i]: (Y0)))))),
% 0.21/0.28 inference(fool_elimination,[],[f12])).
% 0.21/0.28 thf(f14,plain,(
% 0.21/0.28 (? [X0 : $o] : (($true = X0) & (((in @ emptyset @ (prop2set @ X0))) != $true)) & (powersetI = $true)) & (dsetconstrI = $true)),
% 0.21/0.28 inference(ennf_transformation,[],[f9])).
% 0.21/0.28 thf(f15,plain,(
% 0.21/0.28 (dsetconstrI = $true) & ? [X0 : $o] : (($true = X0) & (((in @ emptyset @ (prop2set @ X0))) != $true)) & (powersetI = $true)),
% 0.21/0.28 inference(flattening,[],[f14])).
% 0.21/0.28 thf(f16,plain,(
% 0.21/0.28 ! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)) | (((in @ X1 @ (powerset @ X0))) = $true)) <=> (powersetI = $true)),
% 0.21/0.28 inference(ennf_transformation,[],[f11])).
% 0.21/0.28 thf(f17,plain,(
% 0.21/0.28 (dsetconstrI = $true) <=> ! [X0 : ($i > $o),X2 : $i,X1 : $i] : (((((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true) | (((X0 @ X2)) != $true)) | (((in @ X2 @ X1)) != $true))),
% 0.21/0.28 inference(ennf_transformation,[],[f7])).
% 0.21/0.28 thf(f18,plain,(
% 0.21/0.28 (dsetconstrI = $true) <=> ! [X2 : $i,X0 : ($i > $o),X1 : $i] : ((((X0 @ X2)) != $true) | (((in @ X2 @ X1)) != $true) | (((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true))),
% 0.21/0.28 inference(flattening,[],[f17])).
% 0.21/0.28 thf(f19,plain,(
% 0.21/0.28 (! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)) | (((in @ X1 @ (powerset @ X0))) = $true)) | (powersetI != $true)) & ((powersetI = $true) | ? [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) & (((in @ X1 @ (powerset @ X0))) != $true)))),
% 0.21/0.28 inference(nnf_transformation,[],[f16])).
% 0.21/0.28 thf(f20,plain,(
% 0.21/0.28 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | ($true = ((in @ X0 @ (powerset @ X1))))) | (powersetI != $true)) & ((powersetI = $true) | ? [X3 : $i,X4 : $i] : (! [X5 : $i] : ((((in @ X5 @ X4)) = $true) | (((in @ X5 @ X3)) != $true)) & (((in @ X3 @ (powerset @ X4))) != $true)))),
% 0.21/0.28 inference(rectify,[],[f19])).
% 0.21/0.28 thf(f21,plain,(
% 0.21/0.28 (! [X0 : $i,X1 : $i] : ((($true != ((in @ (sK0 @ X1 @ X0) @ X1))) & (((in @ (sK0 @ X1 @ X0) @ X0)) = $true)) | ($true = ((in @ X0 @ (powerset @ X1))))) | (powersetI != $true)) & ((powersetI = $true) | (! [X5 : $i] : (($true = ((in @ X5 @ sK2))) | (((in @ X5 @ sK1)) != $true)) & ($true != ((in @ sK1 @ (powerset @ sK2))))))),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK1,sK2]),skolemize(X2,sK0 @ X1 @ X0),skolemize(X3,sK1),skolemize(X4,sK2)],[f20])).
% 0.21/0.28 thf(f22,plain,(
% 0.21/0.28 (dsetconstrI = $true) & (($true = sK3) & ($true != ((in @ emptyset @ (prop2set @ sK3))))) & (powersetI = $true)),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f15])).
% 0.21/0.28 thf(f23,plain,(
% 0.21/0.28 ((dsetconstrI = $true) | ? [X2 : $i,X0 : ($i > $o),X1 : $i] : ((((X0 @ X2)) = $true) & (((in @ X2 @ X1)) = $true) & (((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) != $true))) & (! [X2 : $i,X0 : ($i > $o),X1 : $i] : ((((X0 @ X2)) != $true) | (((in @ X2 @ X1)) != $true) | (((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true)) | (dsetconstrI != $true))),
% 0.21/0.28 inference(nnf_transformation,[],[f18])).
% 0.21/0.28 thf(f24,plain,(
% 0.21/0.28 ((dsetconstrI = $true) | ? [X0 : $i,X1 : ($i > $o),X2 : $i] : ((((X1 @ X0)) = $true) & ($true = ((in @ X0 @ X2))) & (((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0))))) != $true))) & (! [X3 : $i,X4 : ($i > $o),X5 : $i] : (($true != ((X4 @ X3))) | (((in @ X3 @ X5)) != $true) | (((in @ X3 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X4 @ Y0))))) = $true)) | (dsetconstrI != $true))),
% 0.21/0.28 inference(rectify,[],[f23])).
% 0.21/0.28 thf(f25,plain,(
% 0.21/0.28 ((dsetconstrI = $true) | ((((sK5 @ sK4)) = $true) & ($true = ((in @ sK4 @ sK6))) & (((in @ sK4 @ (dsetconstr @ sK6 @ (^[Y0 : $i]: (sK5 @ Y0))))) != $true))) & (! [X3 : $i,X4 : ($i > $o),X5 : $i] : (($true != ((X4 @ X3))) | (((in @ X3 @ X5)) != $true) | (((in @ X3 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X4 @ Y0))))) = $true)) | (dsetconstrI != $true))),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f24])).
% 0.21/0.28 thf(f28,plain,(
% 0.21/0.28 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) | (((in @ (sK0 @ X1 @ X0) @ X0)) = $true) | (powersetI != $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f21])).
% 0.21/0.28 thf(f29,plain,(
% 0.21/0.28 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) | (powersetI != $true) | ($true != ((in @ (sK0 @ X1 @ X0) @ X1)))) )),
% 0.21/0.28 inference(cnf_transformation,[],[f21])).
% 0.21/0.28 thf(f30,plain,(
% 0.21/0.28 (powersetI = $true)),
% 0.21/0.28 inference(cnf_transformation,[],[f22])).
% 0.21/0.28 thf(f31,plain,(
% 0.21/0.28 ($true != ((in @ emptyset @ (prop2set @ sK3))))),
% 0.21/0.28 inference(cnf_transformation,[],[f22])).
% 0.21/0.28 thf(f32,plain,(
% 0.21/0.28 ($true = sK3)),
% 0.21/0.28 inference(cnf_transformation,[],[f22])).
% 0.21/0.28 thf(f33,plain,(
% 0.21/0.28 (dsetconstrI = $true)),
% 0.21/0.28 inference(cnf_transformation,[],[f22])).
% 0.21/0.28 thf(f34,plain,(
% 0.21/0.28 (prop2set = (^[Y0 : $o]: (dsetconstr @ (powerset @ emptyset) @ (^[Y1 : $i]: (Y0)))))),
% 0.21/0.28 inference(cnf_transformation,[],[f13])).
% 0.21/0.28 thf(f35,plain,(
% 0.21/0.28 ( ! [X3 : $i,X4 : ($i > $o),X5 : $i] : ((((in @ X3 @ X5)) != $true) | (((in @ X3 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X4 @ Y0))))) = $true) | (dsetconstrI != $true) | ($true != ((X4 @ X3)))) )),
% 0.21/0.28 inference(cnf_transformation,[],[f25])).
% 0.21/0.28 thf(f40,plain,(
% 0.21/0.28 ( ! [X3 : $i,X4 : ($i > $o),X5 : $i] : ((((in @ X3 @ X5)) != $true) | ($true != ((X4 @ X3))) | (((in @ X3 @ (dsetconstr @ X5 @ X4))) = $true) | (dsetconstrI != $true)) )),
% 0.21/0.28 inference(beta-eta_normalization,[],[f35])).
% 0.21/0.28 thf(f43,definition,(
% 0.21/0.28 spl7_1 <=> (powersetI = $true)),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition])).
% 0.21/0.28 thf(f46,plain,(
% 0.21/0.28 spl7_1),
% 0.21/0.28 inference(avatar_split_clause,[],[f30,f43])).
% 0.21/0.28 thf(f48,definition,(
% 0.21/0.28 spl7_2 <=> ($true = sK3)),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition])).
% 0.21/0.28 thf(f50,plain,(
% 0.21/0.28 ($true = sK3) | ~spl7_2),
% 0.21/0.28 inference(avatar_component_clause,[],[f48])).
% 0.21/0.28 thf(f51,plain,(
% 0.21/0.28 spl7_2),
% 0.21/0.28 inference(avatar_split_clause,[],[f32,f48])).
% 0.21/0.28 thf(f53,definition,(
% 0.21/0.28 spl7_3 <=> (dsetconstrI = $true)),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition])).
% 0.21/0.28 thf(f62,definition,(
% 0.21/0.28 spl7_5 <=> ! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) | ($true != ((in @ (sK0 @ X1 @ X0) @ X1))))),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition])).
% 0.21/0.28 thf(f63,plain,(
% 0.21/0.28 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK0 @ X1 @ X0) @ X1))) | ($true = ((in @ X0 @ (powerset @ X1))))) ) | ~spl7_5),
% 0.21/0.28 inference(avatar_component_clause,[],[f62])).
% 0.21/0.28 thf(f64,plain,(
% 0.21/0.28 ~spl7_1 | spl7_5),
% 0.21/0.28 inference(avatar_split_clause,[],[f29,f62,f43])).
% 0.21/0.28 thf(f70,definition,(
% 0.21/0.28 spl7_7 <=> ! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) | (((in @ (sK0 @ X1 @ X0) @ X0)) = $true))),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition])).
% 0.21/0.28 thf(f71,plain,(
% 0.21/0.28 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK0 @ X1 @ X0) @ X0)) = $true) | ($true = ((in @ X0 @ (powerset @ X1))))) ) | ~spl7_7),
% 0.21/0.28 inference(avatar_component_clause,[],[f70])).
% 0.21/0.28 thf(f72,plain,(
% 0.21/0.28 ~spl7_1 | spl7_7),
% 0.21/0.28 inference(avatar_split_clause,[],[f28,f70,f43])).
% 0.21/0.28 thf(f74,definition,(
% 0.21/0.28 spl7_8 <=> (prop2set = (^[Y0 : $o]: (dsetconstr @ (powerset @ emptyset) @ (^[Y1 : $i]: (Y0)))))),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition])).
% 0.21/0.28 thf(f76,plain,(
% 0.21/0.28 (prop2set = (^[Y0 : $o]: (dsetconstr @ (powerset @ emptyset) @ (^[Y1 : $i]: (Y0))))) | ~spl7_8),
% 0.21/0.28 inference(avatar_component_clause,[],[f74])).
% 0.21/0.28 thf(f77,plain,(
% 0.21/0.28 spl7_8),
% 0.21/0.28 inference(avatar_split_clause,[],[f34,f74])).
% 0.21/0.28 thf(f79,definition,(
% 0.21/0.28 spl7_9 <=> ($true = ((in @ emptyset @ (prop2set @ sK3))))),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl7_9])],[avatar_definition])).
% 0.21/0.28 thf(f81,plain,(
% 0.21/0.28 ($true != ((in @ emptyset @ (prop2set @ sK3)))) | spl7_9),
% 0.21/0.28 inference(avatar_component_clause,[],[f79])).
% 0.21/0.28 thf(f82,plain,(
% 0.21/0.28 ~spl7_9),
% 0.21/0.28 inference(avatar_split_clause,[],[f31,f79])).
% 0.21/0.28 thf(f84,definition,(
% 0.21/0.28 spl7_10 <=> ! [X4 : ($i > $o),X5 : $i,X3 : $i] : ((((in @ X3 @ X5)) != $true) | (((in @ X3 @ (dsetconstr @ X5 @ X4))) = $true) | ($true != ((X4 @ X3))))),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl7_10])],[avatar_definition])).
% 0.21/0.28 thf(f85,plain,(
% 0.21/0.28 ( ! [X3 : $i,X4 : ($i > $o),X5 : $i] : ((((in @ X3 @ (dsetconstr @ X5 @ X4))) = $true) | (((in @ X3 @ X5)) != $true) | ($true != ((X4 @ X3)))) ) | ~spl7_10),
% 0.21/0.28 inference(avatar_component_clause,[],[f84])).
% 0.21/0.28 thf(f86,plain,(
% 0.21/0.28 ~spl7_3 | spl7_10),
% 0.21/0.28 inference(avatar_split_clause,[],[f40,f84,f53])).
% 0.21/0.28 thf(f102,plain,(
% 0.21/0.28 spl7_3),
% 0.21/0.28 inference(avatar_split_clause,[],[f33,f53])).
% 0.21/0.28 thf(f120,plain,(
% 0.21/0.28 ( ! [X0 : $i] : ((((in @ X0 @ (powerset @ X0))) = $true) | ($true != $true) | (((in @ X0 @ (powerset @ X0))) = $true)) ) | (~spl7_5 | ~spl7_7)),
% 0.21/0.28 inference(superposition,[],[f63,f71])).
% 0.21/0.28 thf(f121,plain,(
% 0.21/0.28 ( ! [X0 : $i] : (($true != $true) | (((in @ X0 @ (powerset @ X0))) = $true)) ) | (~spl7_5 | ~spl7_7)),
% 0.21/0.28 inference(duplicate_literal_removal,[],[f120])).
% 0.21/0.28 thf(f122,plain,(
% 0.21/0.28 ( ! [X0 : $i] : ((((in @ X0 @ (powerset @ X0))) = $true)) ) | (~spl7_5 | ~spl7_7)),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f121])).
% 0.21/0.28 thf(f123,plain,(
% 0.21/0.28 ( ! [X1 : $o] : ((((prop2set @ X1)) = (((^[Y0 : $o]: (dsetconstr @ (powerset @ emptyset) @ (^[Y1 : $i]: (Y0)))) @ X1)))) ) | ~spl7_8),
% 0.21/0.28 inference(argument_congruence,[],[f76])).
% 0.21/0.28 thf(f124,plain,(
% 0.21/0.28 ( ! [X1 : $o] : ((((prop2set @ X1)) = ((dsetconstr @ (powerset @ emptyset) @ (^[Y0 : $i]: (X1)))))) ) | ~spl7_8),
% 0.21/0.28 inference(beta-eta_normalization,[],[f123])).
% 0.21/0.28 thf(f131,plain,(
% 0.21/0.28 ( ! [X0 : $o,X1 : $i] : (($true != ((in @ X1 @ (powerset @ emptyset)))) | ($true = ((in @ X1 @ (prop2set @ X0)))) | ((((^[Y0 : $i]: (X0)) @ X1)) != $true)) ) | (~spl7_8 | ~spl7_10)),
% 0.21/0.28 inference(superposition,[],[f85,f124])).
% 0.21/0.28 thf(f134,plain,(
% 0.21/0.28 ( ! [X0 : $o,X1 : $i] : (($true = ((in @ X1 @ (prop2set @ X0)))) | ($true != X0) | ($true != ((in @ X1 @ (powerset @ emptyset))))) ) | (~spl7_8 | ~spl7_10)),
% 0.21/0.28 inference(beta-eta_normalization,[],[f131])).
% 0.21/0.28 thf(f136,plain,(
% 0.21/0.28 ($true != sK3) | (((in @ emptyset @ (powerset @ emptyset))) != $true) | ($true != $true) | (~spl7_8 | spl7_9 | ~spl7_10)),
% 0.21/0.28 inference(superposition,[],[f81,f134])).
% 0.21/0.28 thf(f139,plain,(
% 0.21/0.28 (((in @ emptyset @ (powerset @ emptyset))) != $true) | ($true != sK3) | (~spl7_8 | spl7_9 | ~spl7_10)),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f136])).
% 0.21/0.28 thf(f140,plain,(
% 0.21/0.28 ($true != sK3) | (~spl7_5 | ~spl7_7 | ~spl7_8 | spl7_9 | ~spl7_10)),
% 0.21/0.28 inference(forward_subsumption_resolution,[],[f139,f122])).
% 0.21/0.28 thf(f141,plain,(
% 0.21/0.28 $false | (~spl7_2 | ~spl7_5 | ~spl7_7 | ~spl7_8 | spl7_9 | ~spl7_10)),
% 0.21/0.28 inference(forward_subsumption_resolution,[],[f140,f50])).
% 0.21/0.28 thf(f142,plain,(
% 0.21/0.28 ~spl7_2 | ~spl7_5 | ~spl7_7 | ~spl7_8 | spl7_9 | ~spl7_10),
% 0.21/0.28 inference(avatar_contradiction_clause,[],[f141])).
% 0.21/0.28 cnf(s1, plain, spl7_1, inference(sat_conversion,[],[f46])).
% 0.21/0.28 cnf(s2, plain, spl7_2, inference(sat_conversion,[],[f51])).
% 0.21/0.28 cnf(s4, plain, ~spl7_1 | spl7_5, inference(sat_conversion,[],[f64])).
% 0.21/0.28 cnf(s6, plain, ~spl7_1 | spl7_7, inference(sat_conversion,[],[f72])).
% 0.21/0.28 cnf(s7, plain, spl7_8, inference(sat_conversion,[],[f77])).
% 0.21/0.28 cnf(s8, plain, ~spl7_9, inference(sat_conversion,[],[f82])).
% 0.21/0.28 cnf(s9, plain, ~spl7_3 | spl7_10, inference(sat_conversion,[],[f86])).
% 0.21/0.28 cnf(s13, plain, spl7_3, inference(sat_conversion,[],[f102])).
% 0.21/0.28 cnf(s18, plain, ~spl7_2 | ~spl7_5 | ~spl7_7 | ~spl7_8 | spl7_9 | ~spl7_10, inference(sat_conversion,[],[f142])).
% 0.21/0.28 cnf(s19, plain, spl7_10, inference(rat,[],[s9,s13])).
% 0.21/0.28 cnf(s22, plain, spl7_7, inference(rat,[],[s6,s1])).
% 0.21/0.28 cnf(s23, plain, spl7_5, inference(rat,[],[s4,s1])).
% 0.21/0.28 cnf(s24, plain, $false, inference(rat,[],[s18,s19,s8,s7,s2,s22,s23])).
% 0.21/0.28 thf(f143,plain,(
% 0.21/0.28 $false),
% 0.21/0.28 inference(avatar_sat_refutation,[],[s24])).
% 0.21/0.28 % SZS output end Proof for theBenchmark
% 0.21/0.28 % (1315916)------------------------------
% 0.21/0.28 % (1315916)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (1315916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (1315916)CaDiCaL version: 2.1.3
% 0.21/0.28 % (1315916)Termination reason: Refutation
% 0.21/0.28 % (1315916)Time elapsed: 0.004 s
% 0.21/0.28 % (1315916)Peak memory usage: 13 MB
% 0.21/0.28 % (1315916)Instructions burned: 8 (million)
% 0.21/0.28 % (1315908)Success in time 0.029 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------