%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU518^2 : 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 : n009.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 0.23s 0.28s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU518^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n009.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:48:00 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.23/0.28 % (4018174)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.28 % (4018192)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2093959212:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.28 % (4018192) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4018174-4018192"...
% 0.23/0.28 % (4018192)...printing done.
% 0.23/0.28 % (4018192)Refutation found. Thanks to Tanya!
% 0.23/0.28 % SZS status Theorem for theBenchmark
% 0.23/0.28 % SZS output start Proof for theBenchmark
% 0.23/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.28 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.23/0.28 thf(func_def_1, type, powerset: ($i > $i)).
% 0.23/0.28 thf(func_def_2, type, powersetAx: $o).
% 0.23/0.28 thf(func_def_11, type, sK5: ($i > $i > $i)).
% 0.23/0.28 thf(f1,axiom,(
% 0.23/0.28 (powersetAx = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) <=> (in @ X1 @ (powerset @ X0))))),
% 0.23/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx)).
% 0.23/0.28 thf(f2,conjecture,(
% 0.23/0.28 powersetAx => ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0)))),
% 0.23/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI)).
% 0.23/0.28 thf(f3,negated_conjecture,(
% 0.23/0.28 ~(powersetAx => ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))))),
% 0.23/0.28 inference(negated_conjecture,[status(cth)],[f2])).
% 0.23/0.28 thf(f4,plain,(
% 0.23/0.28 (powersetAx = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) <=> (in @ X1 @ (powerset @ X0))))),
% 0.23/0.28 inference(rectify,[],[f1])).
% 0.23/0.28 thf(f5,plain,(
% 0.23/0.28 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) <=> (((in @ X1 @ (powerset @ X0))) = $true)) <=> (powersetAx = $true)),
% 0.23/0.28 inference(fool_elimination,[],[f4])).
% 0.23/0.28 thf(f6,plain,(
% 0.23/0.28 ~(powersetAx => ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (in @ X0 @ (powerset @ X1))))),
% 0.23/0.28 inference(rectify,[],[f3])).
% 0.23/0.28 thf(f7,plain,(
% 0.23/0.28 ~((powersetAx = $true) => ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => ($true = ((in @ X0 @ (powerset @ X1))))))),
% 0.23/0.28 inference(fool_elimination,[],[f6])).
% 0.23/0.28 thf(f8,plain,(
% 0.23/0.28 (powersetAx = $true) <=> ! [X1 : $i,X0 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) <=> ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)))),
% 0.23/0.28 inference(ennf_transformation,[],[f5])).
% 0.23/0.28 thf(f9,plain,(
% 0.23/0.28 (powersetAx = $true) & ? [X1 : $i,X0 : $i] : (($true != ((in @ X0 @ (powerset @ X1)))) & ! [X2 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X2 @ X1)) = $true)))),
% 0.23/0.28 inference(ennf_transformation,[],[f7])).
% 0.23/0.28 thf(f10,plain,(
% 0.23/0.28 (powersetAx = $true) & ? [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) & ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)))),
% 0.23/0.28 inference(rectify,[],[f9])).
% 0.23/0.28 thf(f11,plain,(
% 0.23/0.28 (powersetAx = $true) & (($true != ((in @ sK1 @ (powerset @ sK0)))) & ! [X2 : $i] : (($true != ((in @ X2 @ sK1))) | ($true = ((in @ X2 @ sK0)))))),
% 0.23/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f10])).
% 0.23/0.28 thf(f12,plain,(
% 0.23/0.28 ((powersetAx = $true) | ? [X1 : $i,X0 : $i] : ((? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true)) | (((in @ X1 @ (powerset @ X0))) != $true)) & (! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)) | (((in @ X1 @ (powerset @ X0))) = $true)))) & (! [X1 : $i,X0 : $i] : (((((in @ X1 @ (powerset @ X0))) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true))) & (! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)) | (((in @ X1 @ (powerset @ X0))) != $true))) | (powersetAx != $true))),
% 0.23/0.28 inference(nnf_transformation,[],[f8])).
% 0.23/0.28 thf(f13,plain,(
% 0.23/0.28 ((powersetAx = $true) | ? [X0 : $i,X1 : $i] : ((? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true)) | ($true != ((in @ X0 @ (powerset @ X1))))) & (! [X3 : $i] : (($true != ((in @ X3 @ X0))) | ($true = ((in @ X3 @ X1)))) | ($true = ((in @ X0 @ (powerset @ X1))))))) & (! [X4 : $i,X5 : $i] : (((((in @ X4 @ (powerset @ X5))) = $true) | ? [X6 : $i] : ((((in @ X6 @ X4)) = $true) & ($true != ((in @ X6 @ X5))))) & (! [X7 : $i] : (($true != ((in @ X7 @ X4))) | ($true = ((in @ X7 @ X5)))) | (((in @ X4 @ (powerset @ X5))) != $true))) | (powersetAx != $true))),
% 0.23/0.28 inference(rectify,[],[f12])).
% 0.23/0.28 thf(f14,plain,(
% 0.23/0.28 ((powersetAx = $true) | (((($true = ((in @ sK4 @ sK2))) & ($true != ((in @ sK4 @ sK3)))) | ($true != ((in @ sK2 @ (powerset @ sK3))))) & (! [X3 : $i] : (($true != ((in @ X3 @ sK2))) | ($true = ((in @ X3 @ sK3)))) | ($true = ((in @ sK2 @ (powerset @ sK3))))))) & (! [X4 : $i,X5 : $i] : (((((in @ X4 @ (powerset @ X5))) = $true) | (($true = ((in @ (sK5 @ X5 @ X4) @ X4))) & ($true != ((in @ (sK5 @ X5 @ X4) @ X5))))) & (! [X7 : $i] : (($true != ((in @ X7 @ X4))) | ($true = ((in @ X7 @ X5)))) | (((in @ X4 @ (powerset @ X5))) != $true))) | (powersetAx != $true))),
% 0.23/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,vAPP]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X6,sK5 @ X5 @ X4)],[f13])).
% 0.23/0.28 thf(f15,plain,(
% 0.23/0.28 ( ! [X2 : $i] : (($true != ((in @ X2 @ sK1))) | ($true = ((in @ X2 @ sK0)))) )),
% 0.23/0.28 inference(cnf_transformation,[],[f11])).
% 0.23/0.28 thf(f16,plain,(
% 0.23/0.28 ($true != ((in @ sK1 @ (powerset @ sK0))))),
% 0.23/0.28 inference(cnf_transformation,[],[f11])).
% 0.23/0.28 thf(f17,plain,(
% 0.23/0.28 (powersetAx = $true)),
% 0.23/0.28 inference(cnf_transformation,[],[f11])).
% 0.23/0.28 thf(f19,plain,(
% 0.23/0.28 ( ! [X4 : $i,X5 : $i] : ((((in @ X4 @ (powerset @ X5))) = $true) | (powersetAx != $true) | ($true != ((in @ (sK5 @ X5 @ X4) @ X5)))) )),
% 0.23/0.28 inference(cnf_transformation,[],[f14])).
% 0.23/0.28 thf(f20,plain,(
% 0.23/0.28 ( ! [X4 : $i,X5 : $i] : ((((in @ X4 @ (powerset @ X5))) = $true) | ($true = ((in @ (sK5 @ X5 @ X4) @ X4))) | (powersetAx != $true)) )),
% 0.23/0.28 inference(cnf_transformation,[],[f14])).
% 0.23/0.28 thf(f26,plain,(
% 0.23/0.28 ( ! [X4 : $i,X5 : $i] : (($true != ((in @ (sK5 @ X5 @ X4) @ X5))) | (((in @ X4 @ (powerset @ X5))) = $true)) )),
% 0.23/0.28 inference(forward_subsumption_resolution,[],[f19,f17])).
% 0.23/0.28 thf(f27,plain,(
% 0.23/0.28 ( ! [X4 : $i,X5 : $i] : (($true = ((in @ (sK5 @ X5 @ X4) @ X4))) | (((in @ X4 @ (powerset @ X5))) = $true)) )),
% 0.23/0.28 inference(forward_subsumption_resolution,[],[f20,f17])).
% 0.23/0.28 thf(f29,plain,(
% 0.23/0.28 ( ! [X0 : $i] : (($true = ((in @ (sK5 @ X0 @ sK1) @ sK0))) | ($true = ((in @ sK1 @ (powerset @ X0)))) | ($true != $true)) )),
% 0.23/0.28 inference(superposition,[],[f15,f27])).
% 0.23/0.28 thf(f30,plain,(
% 0.23/0.28 ( ! [X0 : $i] : (($true = ((in @ (sK5 @ X0 @ sK1) @ sK0))) | ($true = ((in @ sK1 @ (powerset @ X0))))) )),
% 0.23/0.28 inference(trivial_inequality_removal,[],[f29])).
% 0.23/0.28 thf(f34,plain,(
% 0.23/0.28 ($true = ((in @ sK1 @ (powerset @ sK0)))) | ($true != $true) | ($true = ((in @ sK1 @ (powerset @ sK0))))),
% 0.23/0.28 inference(superposition,[],[f26,f30])).
% 0.23/0.28 thf(f35,plain,(
% 0.23/0.28 ($true = ((in @ sK1 @ (powerset @ sK0)))) | ($true != $true)),
% 0.23/0.28 inference(duplicate_literal_removal,[],[f34])).
% 0.23/0.28 thf(f36,plain,(
% 0.23/0.28 ($true = ((in @ sK1 @ (powerset @ sK0))))),
% 0.23/0.28 inference(trivial_inequality_removal,[],[f35])).
% 0.23/0.28 thf(f37,plain,(
% 0.23/0.28 $false),
% 0.23/0.28 inference(forward_subsumption_resolution,[],[f36,f16])).
% 0.23/0.28 % SZS output end Proof for theBenchmark
% 0.23/0.28 % (4018192)------------------------------
% 0.23/0.28 % (4018192)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.28 % (4018192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.28 % (4018192)CaDiCaL version: 2.1.3
% 0.23/0.28 % (4018192)Termination reason: Refutation
% 0.23/0.28 % (4018192)Time elapsed: 0.002 s
% 0.23/0.28 % (4018192)Peak memory usage: 12 MB
% 0.23/0.28 % (4018192)Instructions burned: 4 (million)
% 0.23/0.28 % (4018174)Success in time 0.03 s
% 0.23/0.28 % Vampire exiting
%------------------------------------------------------------------------------