%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU519^2 : 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 : n008.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 08:29:54 AM UTC 2026
% Result : Theorem 0.25s 0.34s
% Output : Refutation 0.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU519^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n008.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 13:48:24 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 Running higher-order theorem proving
% 0.09/0.27 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
% 0.25/0.34 % (3178994)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.34 % (3179002)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=2898806450: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)
% 0.25/0.34 % (3179002)Refutation not found, incomplete strategy
% 0.25/0.34 % (3179002)------------------------------
% 0.25/0.34 % (3179002)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.34 % (3179002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.34 % (3179002)CaDiCaL version: 2.1.3
% 0.25/0.34 % (3179002)Termination reason: Refutation not found, incomplete strategy
% 0.25/0.34 % (3179002)Time elapsed: 0.003 s
% 0.25/0.34 % (3179002)Peak memory usage: 12 MB
% 0.25/0.34 % (3179002)Instructions burned: 3 (million)
% 0.25/0.34 % (3179002)------------------------------
% 0.25/0.34 % (3179002)------------------------------
% 0.25/0.34 % (3179001)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1825276702:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.25/0.34 % (3179000)lrs+10_16_si=on:nwc=1.5:random_seed=4224628230:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.25/0.34 % (3178999)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2319850566:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.25/0.34 % (3179003)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2894053153:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.25/0.34 % (3179004)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2462090137:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.25/0.34 % (3179001)Refutation not found, incomplete strategy
% 0.25/0.34 % (3179001)------------------------------
% 0.25/0.34 % (3179001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.34 % (3179001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.34 % (3179001)CaDiCaL version: 2.1.3
% 0.25/0.34 % (3179001)Termination reason: Refutation not found, incomplete strategy
% 0.25/0.34 % (3179001)Time elapsed: 0.002 s
% 0.25/0.34 % (3179001)Peak memory usage: 12 MB
% 0.25/0.34 % (3179001)Instructions burned: 1 (million)
% 0.25/0.34 % (3178999) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3178994-3178999"...
% 0.25/0.34 % (3179001)------------------------------
% 0.25/0.34 % (3179001)------------------------------
% 0.25/0.34 % (3179003) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3178994-3179003"...
% 0.25/0.34 % (3179004) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3178994-3179004"...
% 0.25/0.34 % (3179000) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3178994-3179000"...
% 0.25/0.34 % (3179004)...printing done.
% 0.25/0.34 % (3179004)Refutation found. Thanks to Tanya!
% 0.25/0.34 % SZS status Theorem for theBenchmark
% 0.25/0.34 % SZS output start Proof for theBenchmark
% 0.25/0.34 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.25/0.34 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.25/0.34 thf(func_def_2, type, powerset: ($i > $i)).
% 0.25/0.34 thf(func_def_3, type, emptysetE: $o).
% 0.25/0.34 thf(func_def_5, type, powersetI: $o).
% 0.25/0.34 thf(func_def_10, type, sK2: $o).
% 0.25/0.34 thf(func_def_11, type, sK3: ($i > $i > $i)).
% 0.25/0.34 thf(func_def_14, type, vNOT: ($o > $o)).
% 0.25/0.34 thf(f1,axiom,(
% 0.25/0.34 (! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1) = emptysetE)),
% 0.25/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE)).
% 0.25/0.34 thf(f2,axiom,(
% 0.25/0.34 (powersetI = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))))),
% 0.25/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI)).
% 0.25/0.34 thf(f3,conjecture,(
% 0.25/0.34 emptysetE => (powersetI => ! [X0 : $i] : (in @ emptyset @ (powerset @ X0)))),
% 0.25/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset)).
% 0.25/0.34 thf(f4,negated_conjecture,(
% 0.25/0.34 ~(emptysetE => (powersetI => ! [X0 : $i] : (in @ emptyset @ (powerset @ X0))))),
% 0.25/0.34 inference(negated_conjecture,[status(cth)],[f3])).
% 0.25/0.34 thf(f5,plain,(
% 0.25/0.34 (! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1) = emptysetE)),
% 0.25/0.34 inference(rectify,[],[f1])).
% 0.25/0.34 thf(f6,plain,(
% 0.25/0.34 ! [X0 : $i] : ((((in @ X0 @ emptyset)) = $true) => ! [X1 : $o] : ($true = X1)) <=> (emptysetE = $true)),
% 0.25/0.34 inference(fool_elimination,[],[f5])).
% 0.25/0.34 thf(f7,plain,(
% 0.25/0.34 ~(emptysetE => (powersetI => ! [X0 : $i] : (in @ emptyset @ (powerset @ X0))))),
% 0.25/0.34 inference(rectify,[],[f4])).
% 0.25/0.34 thf(f8,plain,(
% 0.25/0.34 ~((emptysetE = $true) => ((powersetI = $true) => ! [X0 : $i] : (((in @ emptyset @ (powerset @ X0))) = $true)))),
% 0.25/0.34 inference(fool_elimination,[],[f7])).
% 0.25/0.34 thf(f9,plain,(
% 0.25/0.34 (powersetI = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (in @ X0 @ (powerset @ X1))))),
% 0.25/0.34 inference(rectify,[],[f2])).
% 0.25/0.34 thf(f10,plain,(
% 0.25/0.34 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => ($true = ((in @ X0 @ (powerset @ X1))))) <=> (powersetI = $true)),
% 0.25/0.34 inference(fool_elimination,[],[f9])).
% 0.25/0.34 thf(f11,plain,(
% 0.25/0.34 ! [X0 : $i] : (! [X1 : $o] : ($true = X1) | (((in @ X0 @ emptyset)) != $true)) <=> (emptysetE = $true)),
% 0.25/0.34 inference(ennf_transformation,[],[f6])).
% 0.25/0.34 thf(f12,plain,(
% 0.25/0.34 ! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) | ? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true))) <=> (powersetI = $true)),
% 0.25/0.34 inference(ennf_transformation,[],[f10])).
% 0.25/0.34 thf(f13,plain,(
% 0.25/0.34 (? [X0 : $i] : (((in @ emptyset @ (powerset @ X0))) != $true) & (powersetI = $true)) & (emptysetE = $true)),
% 0.25/0.34 inference(ennf_transformation,[],[f8])).
% 0.25/0.34 thf(f14,plain,(
% 0.25/0.34 ? [X0 : $i] : (((in @ emptyset @ (powerset @ X0))) != $true) & (powersetI = $true) & (emptysetE = $true)),
% 0.25/0.34 inference(flattening,[],[f13])).
% 0.25/0.34 thf(f15,plain,(
% 0.25/0.34 ($true != ((in @ emptyset @ (powerset @ sK0)))) & (powersetI = $true) & (emptysetE = $true)),
% 0.25/0.34 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f14])).
% 0.25/0.34 thf(f16,plain,(
% 0.25/0.34 (! [X0 : $i] : (! [X1 : $o] : ($true = X1) | (((in @ X0 @ emptyset)) != $true)) | (emptysetE != $true)) & ((emptysetE = $true) | ? [X0 : $i] : (? [X1 : $o] : ($true != X1) & (((in @ X0 @ emptyset)) = $true)))),
% 0.25/0.34 inference(nnf_transformation,[],[f11])).
% 0.25/0.34 thf(f17,plain,(
% 0.25/0.34 (! [X0 : $i] : (! [X1 : $o] : ($true = X1) | (((in @ X0 @ emptyset)) != $true)) | (emptysetE != $true)) & ((emptysetE = $true) | ? [X2 : $i] : (? [X3 : $o] : ($true != X3) & (((in @ X2 @ emptyset)) = $true)))),
% 0.25/0.34 inference(rectify,[],[f16])).
% 0.25/0.34 thf(f18,plain,(
% 0.25/0.34 (! [X0 : $i] : (! [X1 : $o] : ($true = X1) | (((in @ X0 @ emptyset)) != $true)) | (emptysetE != $true)) & ((emptysetE = $true) | (($true != sK2) & ($true = ((in @ sK1 @ emptyset)))))),
% 0.25/0.34 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X2,sK1),skolemize(X3,sK2)],[f17])).
% 0.25/0.34 thf(f19,plain,(
% 0.25/0.34 (! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) | ? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true))) | (powersetI != $true)) & ((powersetI = $true) | ? [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (powerset @ X1)))) & ! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true))))),
% 0.25/0.34 inference(nnf_transformation,[],[f12])).
% 0.25/0.34 thf(f20,plain,(
% 0.25/0.34 (! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) | ? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true))) | (powersetI != $true)) & ((powersetI = $true) | ? [X3 : $i,X4 : $i] : ((((in @ X3 @ (powerset @ X4))) != $true) & ! [X5 : $i] : (($true = ((in @ X5 @ X4))) | ($true != ((in @ X5 @ X3))))))),
% 0.25/0.34 inference(rectify,[],[f19])).
% 0.25/0.34 thf(f21,plain,(
% 0.25/0.34 (! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) | (($true != ((in @ (sK3 @ X1 @ X0) @ X1))) & ($true = ((in @ (sK3 @ X1 @ X0) @ X0))))) | (powersetI != $true)) & ((powersetI = $true) | (($true != ((in @ sK4 @ (powerset @ sK5)))) & ! [X5 : $i] : ((((in @ X5 @ sK5)) = $true) | (((in @ X5 @ sK4)) != $true))))),
% 0.25/0.34 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK4,sK5]),skolemize(X2,sK3 @ X1 @ X0),skolemize(X3,sK4),skolemize(X4,sK5)],[f20])).
% 0.25/0.34 thf(f22,plain,(
% 0.25/0.34 (emptysetE = $true)),
% 0.25/0.34 inference(cnf_transformation,[],[f15])).
% 0.25/0.34 thf(f23,plain,(
% 0.25/0.34 (powersetI = $true)),
% 0.25/0.34 inference(cnf_transformation,[],[f15])).
% 0.25/0.34 thf(f24,plain,(
% 0.25/0.34 ($true != ((in @ emptyset @ (powerset @ sK0))))),
% 0.25/0.34 inference(cnf_transformation,[],[f15])).
% 0.25/0.34 thf(f27,plain,(
% 0.25/0.34 ( ! [X0 : $i,X1 : $o] : (($true = X1) | (((in @ X0 @ emptyset)) != $true) | (emptysetE != $true)) )),
% 0.25/0.34 inference(cnf_transformation,[],[f18])).
% 0.25/0.34 thf(f30,plain,(
% 0.25/0.34 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) | ($true = ((in @ (sK3 @ X1 @ X0) @ X0))) | (powersetI != $true)) )),
% 0.25/0.34 inference(cnf_transformation,[],[f21])).
% 0.25/0.34 thf(f34,plain,(
% 0.25/0.34 ( ! [X0 : $i,X1 : $o] : (($true != $true) | ($true = X1) | (((in @ X0 @ emptyset)) != $true)) )),
% 0.25/0.34 inference(definition_unfolding,[],[f27,f22])).
% 0.25/0.34 thf(f38,plain,(
% 0.25/0.34 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK3 @ X1 @ X0) @ X0))) | ($true = ((in @ X0 @ (powerset @ X1)))) | ($true != $true)) )),
% 0.25/0.34 inference(definition_unfolding,[],[f30,f23])).
% 0.25/0.34 thf(f42,plain,(
% 0.25/0.34 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK3 @ X1 @ X0) @ X0))) | ($true = ((in @ X0 @ (powerset @ X1))))) )),
% 0.25/0.34 inference(trivial_inequality_removal,[],[f38])).
% 0.25/0.34 thf(f43,plain,(
% 0.25/0.34 ( ! [X0 : $i,X1 : $o] : (($true = X1) | (((in @ X0 @ emptyset)) != $true)) )),
% 0.25/0.34 inference(trivial_inequality_removal,[],[f34])).
% 0.25/0.34 thf(f45,definition,(
% 0.25/0.34 spl6_1 <=> ! [X0 : $i] : (((in @ X0 @ emptyset)) != $true)),
% 0.25/0.34 introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
% 0.25/0.34 thf(f46,plain,(
% 0.25/0.34 ( ! [X0 : $i] : ((((in @ X0 @ emptyset)) != $true)) ) | ~spl6_1),
% 0.25/0.34 inference(avatar_component_clause,[],[f45])).
% 0.25/0.34 thf(f48,definition,(
% 0.25/0.34 spl6_2 <=> ! [X1 : $o] : ($true = X1)),
% 0.25/0.34 introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
% 0.25/0.34 thf(f49,plain,(
% 0.25/0.34 ( ! [X1 : $o] : (($true = X1)) ) | ~spl6_2),
% 0.25/0.34 inference(avatar_component_clause,[],[f48])).
% 0.25/0.34 thf(f50,plain,(
% 0.25/0.34 spl6_1 | spl6_2),
% 0.25/0.34 inference(avatar_split_clause,[],[f43,f48,f45])).
% 0.25/0.34 thf(f54,plain,(
% 0.25/0.34 ($true != $true) | ~spl6_2),
% 0.25/0.34 inference(constrained_superposition,[],[f24,f49])).
% 0.25/0.34 thf(f55,plain,(
% 0.25/0.34 $false | ~spl6_2),
% 0.25/0.34 inference(trivial_inequality_removal,[],[f54])).
% 0.25/0.34 thf(f56,plain,(
% 0.25/0.34 ~spl6_2),
% 0.25/0.34 inference(avatar_contradiction_clause,[],[f55])).
% 0.25/0.34 thf(f58,plain,(
% 0.25/0.34 ( ! [X0 : $i] : ((((in @ emptyset @ (powerset @ X0))) = $true) | ($true != $true)) ) | ~spl6_1),
% 0.25/0.34 inference(constrained_superposition,[],[f46,f42])).
% 0.25/0.34 thf(f61,plain,(
% 0.25/0.34 ( ! [X0 : $i] : ((((in @ emptyset @ (powerset @ X0))) = $true)) ) | ~spl6_1),
% 0.25/0.34 inference(trivial_inequality_removal,[],[f58])).
% 0.25/0.34 thf(f62,plain,(
% 0.25/0.34 ($true != $true) | ~spl6_1),
% 0.25/0.34 inference(backward_demodulation,[],[f24,f61])).
% 0.25/0.34 thf(f63,plain,(
% 0.25/0.34 $false | ~spl6_1),
% 0.25/0.34 inference(trivial_inequality_removal,[],[f62])).
% 0.25/0.34 thf(f64,plain,(
% 0.25/0.34 ~spl6_1),
% 0.25/0.34 inference(avatar_contradiction_clause,[],[f63])).
% 0.25/0.34 cnf(s1, plain, spl6_1 | spl6_2, inference(sat_conversion,[],[f50])).
% 0.25/0.34 cnf(s2, plain, ~spl6_2, inference(sat_conversion,[],[f56])).
% 0.25/0.34 cnf(s3, plain, ~spl6_1, inference(sat_conversion,[],[f64])).
% 0.25/0.34 cnf(s4, plain, $false, inference(rat,[],[s1,s2,s3])).
% 0.25/0.34 thf(f65,plain,(
% 0.25/0.34 $false),
% 0.25/0.34 inference(avatar_sat_refutation,[],[s4])).
% 0.25/0.34 % SZS output end Proof for theBenchmark
% 0.25/0.34 % (3179004)------------------------------
% 0.25/0.34 % (3179004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.34 % (3179004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.34 % (3179004)CaDiCaL version: 2.1.3
% 0.25/0.34 % (3179004)Termination reason: Refutation
% 0.25/0.34 % (3179004)Time elapsed: 0.003 s
% 0.25/0.34 % (3179004)Peak memory usage: 13 MB
% 0.25/0.34 % (3179004)Instructions burned: 4 (million)
% 0.25/0.34 % (3178994)Success in time 0.053 s
% 0.25/0.34 % Vampire exiting
%------------------------------------------------------------------------------