%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU560^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:30:04 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 : SEU560^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n026.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 13:52:57 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.10/0.25 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 % (626644)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.29 % (626652)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=2157750498: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)
% 0.24/0.29 % (626649)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2298190991:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.29 % (626650)lrs+10_16_si=on:nwc=1.5:random_seed=2201116861:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.29 % (626653)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3783332098:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.24/0.29 % (626651)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=884552652:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.29 % (626652) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-626644-626652"...
% 0.24/0.29 % (626652)...printing done.
% 0.24/0.29 % (626649) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-626644-626649"...
% 0.24/0.29 % (626651)Refutation not found, incomplete strategy
% 0.24/0.29 % (626651)------------------------------
% 0.24/0.29 % (626651)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.29 % (626651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.29 % (626651)CaDiCaL version: 2.1.3
% 0.24/0.29 % (626651)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.29 % (626651)Time elapsed: 0.001 s
% 0.24/0.29 % (626651)Peak memory usage: 12 MB
% 0.24/0.29 % (626651)Instructions burned: 1 (million)
% 0.24/0.29 % (626652)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) > $tType).
% 0.24/0.29 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.24/0.29 thf(func_def_1, type, subset: ($i > $i > $o)).
% 0.24/0.29 thf(func_def_3, type, subsetI1: $o).
% 0.24/0.29 thf(func_def_4, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.24/0.29 thf(func_def_5, type, vIMP: ($o > $o > $o)).
% 0.24/0.29 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.24/0.29 thf(func_def_7, type, db2: !>[X0: $tType]:(X0)).
% 0.24/0.29 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 0.24/0.29 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.24/0.29 thf(func_def_16, type, sK4: ($i > $i > $i)).
% 0.24/0.29 thf(func_def_18, type, sK6: ($i > $i > $i)).
% 0.24/0.29 thf(f2,axiom,(
% 0.24/0.29 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 0.24/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1)).
% 0.24/0.29 thf(f3,conjecture,(
% 0.24/0.29 subsetI1 => ! [X0 : $i,X1 : $i] : ((X0 = X1) => (subset @ X1 @ X0))),
% 0.24/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2)).
% 0.24/0.29 thf(f4,negated_conjecture,(
% 0.24/0.29 ~(subsetI1 => ! [X0 : $i,X1 : $i] : ((X0 = X1) => (subset @ X1 @ X0)))),
% 0.24/0.29 inference(negated_conjecture,[status(cth)],[f3])).
% 0.24/0.29 thf(f7,plain,(
% 0.24/0.29 ~(subsetI1 => ! [X0 : $i,X1 : $i] : ((X0 = X1) => (subset @ X1 @ X0)))),
% 0.24/0.29 inference(rectify,[],[f4])).
% 0.24/0.29 thf(f8,plain,(
% 0.24/0.29 ~((subsetI1 = $true) => ! [X1 : $i,X0 : $i] : ((X0 = X1) => (((subset @ X1 @ X0)) = $true)))),
% 0.24/0.29 inference(fool_elimination,[],[f7])).
% 0.24/0.29 thf(f9,plain,(
% 0.24/0.29 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 0.24/0.29 inference(rectify,[],[f2])).
% 0.24/0.29 thf(f10,plain,(
% 0.24/0.29 (subsetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => (((subset @ X0 @ X1)) = $true))),
% 0.24/0.29 inference(fool_elimination,[],[f9])).
% 0.24/0.29 thf(f11,plain,(
% 0.24/0.29 ? [X1 : $i,X0 : $i] : ((((subset @ X1 @ X0)) != $true) & (X0 = X1)) & (subsetI1 = $true)),
% 0.24/0.29 inference(ennf_transformation,[],[f8])).
% 0.24/0.29 thf(f12,plain,(
% 0.24/0.29 (subsetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | (((subset @ X0 @ X1)) = $true))),
% 0.24/0.29 inference(ennf_transformation,[],[f10])).
% 0.24/0.29 thf(f13,plain,(
% 0.24/0.29 ? [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) & (X0 = X1)) & (subsetI1 = $true)),
% 0.24/0.30 inference(rectify,[],[f11])).
% 0.24/0.30 thf(f14,plain,(
% 0.24/0.30 ((((subset @ sK0 @ sK1)) != $true) & (sK0 = sK1)) & (subsetI1 = $true)),
% 0.24/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f13])).
% 0.24/0.30 thf(f15,plain,(
% 0.24/0.30 ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)) & (((subset @ X0 @ X1)) != $true))) & (! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | (((subset @ X0 @ X1)) = $true)) | (subsetI1 != $true))),
% 0.24/0.30 inference(nnf_transformation,[],[f12])).
% 0.24/0.30 thf(f16,plain,(
% 0.24/0.30 ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)) & (((subset @ X0 @ X1)) != $true))) & (! [X3 : $i,X4 : $i] : (? [X5 : $i] : ((((in @ X5 @ X4)) != $true) & (((in @ X5 @ X3)) = $true)) | (((subset @ X3 @ X4)) = $true)) | (subsetI1 != $true))),
% 0.24/0.30 inference(rectify,[],[f15])).
% 0.24/0.30 thf(f17,plain,(
% 0.24/0.30 ((subsetI1 = $true) | (! [X2 : $i] : (($true = ((in @ X2 @ sK3))) | (((in @ X2 @ sK2)) != $true)) & ($true != ((subset @ sK2 @ sK3))))) & (! [X3 : $i,X4 : $i] : (((((in @ (sK4 @ X4 @ X3) @ X4)) != $true) & (((in @ (sK4 @ X4 @ X3) @ X3)) = $true)) | (((subset @ X3 @ X4)) = $true)) | (subsetI1 != $true))),
% 0.24/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,vAPP]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X5,sK4 @ X4 @ X3)],[f16])).
% 0.24/0.30 thf(f19,plain,(
% 0.24/0.30 (subsetI1 = $true)),
% 0.24/0.30 inference(cnf_transformation,[],[f14])).
% 0.24/0.30 thf(f20,plain,(
% 0.24/0.30 (sK0 = sK1)),
% 0.24/0.30 inference(cnf_transformation,[],[f14])).
% 0.24/0.30 thf(f21,plain,(
% 0.24/0.30 (((subset @ sK0 @ sK1)) != $true)),
% 0.24/0.30 inference(cnf_transformation,[],[f14])).
% 0.24/0.30 thf(f22,plain,(
% 0.24/0.30 ( ! [X3 : $i,X4 : $i] : ((subsetI1 != $true) | (((in @ (sK4 @ X4 @ X3) @ X3)) = $true) | (((subset @ X3 @ X4)) = $true)) )),
% 0.24/0.30 inference(cnf_transformation,[],[f17])).
% 0.24/0.30 thf(f23,plain,(
% 0.24/0.30 ( ! [X3 : $i,X4 : $i] : ((((subset @ X3 @ X4)) = $true) | (subsetI1 != $true) | (((in @ (sK4 @ X4 @ X3) @ X4)) != $true)) )),
% 0.24/0.30 inference(cnf_transformation,[],[f17])).
% 0.24/0.30 thf(f28,definition,(
% 0.24/0.30 spl5_1 <=> (subsetI1 = $true)),
% 0.24/0.30 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 0.24/0.30 thf(f32,definition,(
% 0.24/0.30 spl5_2 <=> ! [X4 : $i,X3 : $i] : ((((in @ (sK4 @ X4 @ X3) @ X3)) = $true) | (((subset @ X3 @ X4)) = $true))),
% 0.24/0.30 introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition])).
% 0.24/0.30 thf(f33,plain,(
% 0.24/0.30 ( ! [X3 : $i,X4 : $i] : ((((in @ (sK4 @ X4 @ X3) @ X3)) = $true) | (((subset @ X3 @ X4)) = $true)) ) | ~spl5_2),
% 0.24/0.30 inference(avatar_component_clause,[],[f32])).
% 0.24/0.30 thf(f34,plain,(
% 0.24/0.30 ~spl5_1 | spl5_2),
% 0.24/0.30 inference(avatar_split_clause,[],[f22,f32,f28])).
% 0.24/0.30 thf(f45,definition,(
% 0.24/0.30 spl5_5 <=> ! [X4 : $i,X3 : $i] : ((((subset @ X3 @ X4)) = $true) | (((in @ (sK4 @ X4 @ X3) @ X4)) != $true))),
% 0.24/0.30 introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition])).
% 0.24/0.30 thf(f46,plain,(
% 0.24/0.30 ( ! [X3 : $i,X4 : $i] : ((((in @ (sK4 @ X4 @ X3) @ X4)) != $true) | (((subset @ X3 @ X4)) = $true)) ) | ~spl5_5),
% 0.24/0.30 inference(avatar_component_clause,[],[f45])).
% 0.24/0.30 thf(f47,plain,(
% 0.24/0.30 spl5_5 | ~spl5_1),
% 0.24/0.30 inference(avatar_split_clause,[],[f23,f28,f45])).
% 0.24/0.30 thf(f53,plain,(
% 0.24/0.30 spl5_1),
% 0.24/0.30 inference(avatar_split_clause,[],[f19,f28])).
% 0.24/0.30 thf(f55,definition,(
% 0.24/0.30 spl5_7 <=> (sK0 = sK1)),
% 0.24/0.30 introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition])).
% 0.24/0.30 thf(f57,plain,(
% 0.24/0.30 (sK0 = sK1) | ~spl5_7),
% 0.24/0.30 inference(avatar_component_clause,[],[f55])).
% 0.24/0.30 thf(f58,plain,(
% 0.24/0.30 spl5_7),
% 0.24/0.30 inference(avatar_split_clause,[],[f20,f55])).
% 0.24/0.30 thf(f60,definition,(
% 0.24/0.30 spl5_8 <=> (((subset @ sK0 @ sK1)) = $true)),
% 0.24/0.30 introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition])).
% 0.24/0.30 thf(f62,plain,(
% 0.24/0.30 (((subset @ sK0 @ sK1)) != $true) | spl5_8),
% 0.24/0.30 inference(avatar_component_clause,[],[f60])).
% 0.24/0.30 thf(f63,plain,(
% 0.24/0.30 ~spl5_8),
% 0.24/0.30 inference(avatar_split_clause,[],[f21,f60])).
% 0.24/0.30 thf(f65,plain,(
% 0.24/0.30 ( ! [X0 : $i] : (($true = ((subset @ X0 @ X0))) | ($true != $true) | ($true = ((subset @ X0 @ X0)))) ) | (~spl5_2 | ~spl5_5)),
% 0.24/0.30 inference(superposition,[],[f46,f33])).
% 0.24/0.30 thf(f66,plain,(
% 0.24/0.30 ( ! [X0 : $i] : (($true != $true) | ($true = ((subset @ X0 @ X0)))) ) | (~spl5_2 | ~spl5_5)),
% 0.24/0.30 inference(duplicate_literal_removal,[],[f65])).
% 0.24/0.30 thf(f67,plain,(
% 0.24/0.30 ( ! [X0 : $i] : (($true = ((subset @ X0 @ X0)))) ) | (~spl5_2 | ~spl5_5)),
% 0.24/0.30 inference(trivial_inequality_removal,[],[f66])).
% 0.24/0.30 thf(f113,plain,(
% 0.24/0.30 (((subset @ sK1 @ sK1)) != $true) | (~spl5_7 | spl5_8)),
% 0.24/0.30 inference(forward_demodulation,[],[f62,f57])).
% 0.24/0.30 thf(f114,plain,(
% 0.24/0.30 $false | (~spl5_2 | ~spl5_5 | ~spl5_7 | spl5_8)),
% 0.24/0.30 inference(forward_subsumption_resolution,[],[f113,f67])).
% 0.24/0.30 thf(f115,plain,(
% 0.24/0.30 ~spl5_2 | ~spl5_5 | ~spl5_7 | spl5_8),
% 0.24/0.30 inference(avatar_contradiction_clause,[],[f114])).
% 0.24/0.30 cnf(s1, plain, ~spl5_1 | spl5_2, inference(sat_conversion,[],[f34])).
% 0.24/0.30 cnf(s4, plain, ~spl5_1 | spl5_5, inference(sat_conversion,[],[f47])).
% 0.24/0.30 cnf(s6, plain, spl5_1, inference(sat_conversion,[],[f53])).
% 0.24/0.30 cnf(s7, plain, spl5_7, inference(sat_conversion,[],[f58])).
% 0.24/0.30 cnf(s8, plain, ~spl5_8, inference(sat_conversion,[],[f63])).
% 0.24/0.30 cnf(s9, plain, ~spl5_2 | ~spl5_5 | ~spl5_7 | spl5_8, inference(sat_conversion,[],[f115])).
% 0.24/0.30 cnf(s10, plain, spl5_5, inference(rat,[],[s4,s6])).
% 0.24/0.30 cnf(s11, plain, ~spl5_2, inference(rat,[],[s9,s8,s7,s10])).
% 0.24/0.30 cnf(s12, plain, $false, inference(rat,[],[s1,s11,s6])).
% 0.24/0.30 thf(f116,plain,(
% 0.24/0.30 $false),
% 0.24/0.30 inference(avatar_sat_refutation,[],[s12])).
% 0.24/0.30 % SZS output end Proof for theBenchmark
% 0.24/0.30 % (626652)------------------------------
% 0.24/0.30 % (626652)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.30 % (626652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.30 % (626652)CaDiCaL version: 2.1.3
% 0.24/0.30 % (626652)Termination reason: Refutation
% 0.24/0.30 % (626652)Time elapsed: 0.003 s
% 0.24/0.30 % (626652)Peak memory usage: 13 MB
% 0.24/0.30 % (626652)Instructions burned: 7 (million)
% 0.24/0.30 % (626644)Success in time 0.036 s
% 0.24/0.30 % Vampire exiting
%------------------------------------------------------------------------------