%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU521^2 : 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 : n014.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 0.21s 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 : SEU521^2 : 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 : n014.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 13:47:45 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 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
% 0.21/0.28 % (2686825)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (2686835)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2184158436:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.28 % (2686835) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2686825-2686835"...
% 0.21/0.28 % (2686835)...printing done.
% 0.21/0.28 % (2686836)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 % (2686836)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 % (2686835)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 > $o)).
% 0.21/0.28 thf(func_def_1, type, powerset: ($i > $i)).
% 0.21/0.28 thf(func_def_2, type, powersetAx: $o).
% 0.21/0.28 thf(func_def_9, type, sK3: ($i > $i > $i)).
% 0.21/0.28 thf(func_def_13, type, vNOT: ($o > $o)).
% 0.21/0.28 thf(f1,axiom,(
% 0.21/0.28 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) <=> (in @ X1 @ (powerset @ X0))) = powersetAx)),
% 0.21/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetAx)).
% 0.21/0.28 thf(f2,conjecture,(
% 0.21/0.28 powersetAx => ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0)))),
% 0.21/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE)).
% 0.21/0.28 thf(f3,negated_conjecture,(
% 0.21/0.28 ~(powersetAx => ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0))))),
% 0.21/0.28 inference(negated_conjecture,[status(cth)],[f2])).
% 0.21/0.28 thf(f4,plain,(
% 0.21/0.28 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) <=> (in @ X1 @ (powerset @ X0))) = powersetAx)),
% 0.21/0.28 inference(rectify,[],[f1])).
% 0.21/0.28 thf(f5,plain,(
% 0.21/0.28 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) <=> (((in @ X1 @ (powerset @ X0))) = $true)) <=> (powersetAx = $true)),
% 0.21/0.29 inference(fool_elimination,[],[f4])).
% 0.21/0.29 thf(f6,plain,(
% 0.21/0.29 ~(powersetAx => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (powerset @ X2)) => ((in @ X1 @ X0) => (in @ X1 @ X2))))),
% 0.21/0.29 inference(rectify,[],[f3])).
% 0.21/0.29 thf(f7,plain,(
% 0.21/0.29 ~((powersetAx = $true) => ! [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X0 @ (powerset @ X2))) = $true) => ((((in @ X1 @ X0)) = $true) => ($true = ((in @ X1 @ X2))))))),
% 0.21/0.29 inference(fool_elimination,[],[f6])).
% 0.21/0.29 thf(f8,plain,(
% 0.21/0.29 ? [X1 : $i,X0 : $i,X2 : $i] : ((($true != ((in @ X1 @ X2))) & (((in @ X1 @ X0)) = $true)) & (((in @ X0 @ (powerset @ X2))) = $true)) & (powersetAx = $true)),
% 0.21/0.29 inference(ennf_transformation,[],[f7])).
% 0.21/0.29 thf(f9,plain,(
% 0.21/0.29 (powersetAx = $true) & ? [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X1 @ X0)) = $true) & (((in @ X0 @ (powerset @ X2))) = $true) & ($true != ((in @ X1 @ X2))))),
% 0.21/0.29 inference(flattening,[],[f8])).
% 0.21/0.29 thf(f10,plain,(
% 0.21/0.29 (powersetAx = $true) <=> ! [X1 : $i,X0 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) <=> ! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)))),
% 0.21/0.29 inference(ennf_transformation,[],[f5])).
% 0.21/0.29 thf(f11,plain,(
% 0.21/0.29 ((powersetAx = $true) | ? [X1 : $i,X0 : $i] : ((? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)) | (((in @ X1 @ (powerset @ X0))) != $true)) & (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) | (((in @ X1 @ (powerset @ X0))) = $true)))) & (! [X1 : $i,X0 : $i] : (((((in @ X1 @ (powerset @ X0))) = $true) | ? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true))) & (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) | (((in @ X1 @ (powerset @ X0))) != $true))) | (powersetAx != $true))),
% 0.21/0.29 inference(nnf_transformation,[],[f10])).
% 0.21/0.29 thf(f12,plain,(
% 0.21/0.29 ((powersetAx = $true) | ? [X0 : $i,X1 : $i] : ((? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | (((in @ X0 @ (powerset @ X1))) != $true)) & (! [X3 : $i] : ((((in @ X3 @ X1)) = $true) | ($true != ((in @ X3 @ X0)))) | (((in @ X0 @ (powerset @ X1))) = $true)))) & (! [X4 : $i,X5 : $i] : ((($true = ((in @ X4 @ (powerset @ X5)))) | ? [X6 : $i] : ((((in @ X6 @ X5)) != $true) & (((in @ X6 @ X4)) = $true))) & (! [X7 : $i] : (($true = ((in @ X7 @ X5))) | ($true != ((in @ X7 @ X4)))) | ($true != ((in @ X4 @ (powerset @ X5)))))) | (powersetAx != $true))),
% 0.21/0.29 inference(rectify,[],[f11])).
% 0.21/0.29 thf(f13,plain,(
% 0.21/0.29 ((powersetAx = $true) | ((((((in @ sK2 @ sK1)) != $true) & (((in @ sK2 @ sK0)) = $true)) | (((in @ sK0 @ (powerset @ sK1))) != $true)) & (! [X3 : $i] : ((((in @ X3 @ sK1)) = $true) | (((in @ X3 @ sK0)) != $true)) | (((in @ sK0 @ (powerset @ sK1))) = $true)))) & (! [X4 : $i,X5 : $i] : ((($true = ((in @ X4 @ (powerset @ X5)))) | (($true != ((in @ (sK3 @ X5 @ X4) @ X5))) & (((in @ (sK3 @ X5 @ X4) @ X4)) = $true))) & (! [X7 : $i] : (($true = ((in @ X7 @ X5))) | ($true != ((in @ X7 @ X4)))) | ($true != ((in @ X4 @ (powerset @ X5)))))) | (powersetAx != $true))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X6,sK3 @ X5 @ X4)],[f12])).
% 0.21/0.29 thf(f14,plain,(
% 0.21/0.29 (powersetAx = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X0 @ (powerset @ X1))) = $true) & (((in @ X2 @ X1)) != $true))),
% 0.21/0.29 inference(rectify,[],[f9])).
% 0.21/0.29 thf(f15,plain,(
% 0.21/0.29 (powersetAx = $true) & ((((in @ sK6 @ sK4)) = $true) & (((in @ sK4 @ (powerset @ sK5))) = $true) & (((in @ sK6 @ sK5)) != $true))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f14])).
% 0.21/0.29 thf(f16,plain,(
% 0.21/0.29 ( ! [X7 : $i,X4 : $i,X5 : $i] : (($true = ((in @ X7 @ X5))) | ($true != ((in @ X7 @ X4))) | ($true != ((in @ X4 @ (powerset @ X5)))) | (powersetAx != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f13])).
% 0.21/0.29 thf(f22,plain,(
% 0.21/0.29 (((in @ sK6 @ sK5)) != $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f15])).
% 0.21/0.29 thf(f23,plain,(
% 0.21/0.29 (((in @ sK4 @ (powerset @ sK5))) = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f15])).
% 0.21/0.29 thf(f24,plain,(
% 0.21/0.29 (((in @ sK6 @ sK4)) = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f15])).
% 0.21/0.29 thf(f25,plain,(
% 0.21/0.29 (powersetAx = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f15])).
% 0.21/0.29 thf(f33,plain,(
% 0.21/0.29 ( ! [X7 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X7 @ X4))) | ($true != $true) | ($true = ((in @ X7 @ X5))) | ($true != ((in @ X4 @ (powerset @ X5))))) )),
% 0.21/0.29 inference(definition_unfolding,[],[f16,f25])).
% 0.21/0.29 thf(f34,plain,(
% 0.21/0.29 ( ! [X7 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X4 @ (powerset @ X5)))) | ($true != ((in @ X7 @ X4))) | ($true = ((in @ X7 @ X5)))) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f33])).
% 0.21/0.29 thf(f42,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true != $true) | (((in @ X0 @ sK4)) != $true) | ($true = ((in @ X0 @ sK5)))) )),
% 0.21/0.29 inference(constrained_superposition,[],[f34,f23])).
% 0.21/0.29 thf(f44,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((((in @ X0 @ sK4)) != $true) | ($true = ((in @ X0 @ sK5)))) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f42])).
% 0.21/0.29 thf(f46,plain,(
% 0.21/0.29 (((in @ sK6 @ sK5)) = $true) | ($true != $true)),
% 0.21/0.29 inference(constrained_superposition,[],[f44,f24])).
% 0.21/0.29 thf(f47,plain,(
% 0.21/0.29 (((in @ sK6 @ sK5)) = $true)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f46])).
% 0.21/0.29 thf(f49,plain,(
% 0.21/0.29 $false),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f47,f22])).
% 0.21/0.29 % SZS output end Proof for theBenchmark
% 0.21/0.29 % (2686835)------------------------------
% 0.21/0.29 % (2686835)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2686835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2686835)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2686835)Termination reason: Refutation
% 0.21/0.29 % (2686835)Time elapsed: 0.002 s
% 0.21/0.29 % (2686835)Peak memory usage: 12 MB
% 0.21/0.29 % (2686835)Instructions burned: 5 (million)
% 0.21/0.29 % (2686825)Success in time 0.028 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------